LU factorization

The sparse matrix-vector multiplication (SpMxV) is a kernel operation widely used in iterative linear solvers. The same sparse matrix is multiplied by a dense vector repeatedly in these solvers. Matrices with irregular sparsity patterns make it difficult to utilize cache locality effectively in SpMxV computations. In this work, we investigate single-and multiple-SpMxV frameworks for exploiting cache locality in SpMxV computations. For the single-SpMxV framework, we propose two cache-size-aware top-down row/column-reordering methods based on 1D and 2D sparse matrix partitioning by utilizing the column-net and enhancing the row-column-net hypergraph models of sparse matrices. The multiple-SpMxV framework depends on splitting a given matrix into a sum of multiple nonzero-disjoint matrices so that the SpMxV operation is performed as a sequence of multiple input-and outputdependent SpMxV operations. For an effective matrix splitting required in this framework, we propose a cachesize-aware top-down approach based on 2D sparse matrix partitioning by utilizing the row-column-net hypergraph model. For this framework, we also propose two methods for effective ordering of individual SpMxV operations. The primary objective in all of the three methods is to maximize the exploitation of temporal locality. We evaluate the validity of our models and methods on a wide range of sparse matrices using both cache-miss simulations and actual runs by using OSKI. Experimental results show that proposed methods and models outperform state-of-the-art schemes.

The capability to rapidly execute the power flow (PF) calculations permit engineers in assured with stay bigger assured within the dependability, protection, and economical operation of their system within the case of planned or unplanned instrumentality failures. The purpose of this work is to investigate the use of FPGA characteristics to speed up power flow computing time for the on-line monitoring system of a power system. The work comprises which is the development of the Power flow program using the Fast-decoupled method based on FPGA (Field Programmable Gate Array), and LABVIEW (graphical programming environment). The program delivered very satisfactory results to solve a 30-bus test system. These findings suggest that in general that differences between the proposed work and the conventional fast decoupled method are satisfactory. As for the execution time, because the FPGA uses parallel solutions, the performance of the proposed method is faster. Also, the engagement of the FPGA and the LabVIEW program presented an effective monitoring system for observing the power system.

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Matrix multiplication is a cornerstone of computational mathematics. Standard algorithms for 2x2 matrices require 8 scalar multiplications, while Strassen's algorithm reduces this to 7. This paper introduces and details Surya Matrix Multiplication, a specialized method tailored for 2x2 symmetric matrices of the circulant form a b b a. We provide a direct algebraic derivation showing that the product can be achieved using only 2 scalar multiplications. This offers a significant computational advantage for this specific matrix structure. The method is compared against standard and Strassen's multiplication, including algorithmic descriptions and Python implementations, to highlight its distinct characteristics and efficiency gains. The resulting product matrix also retains the symmetric circulant form.

For many finite element problems, when represented as sparse matrices, iterative solvers are found to be unreliable because they can impose com-putational bottlenecks. Early pioneering work by Duff et al, explored an alternative strategy called multifrontal sparse matrix factorization. This ap-proach, by representing the sparse problem as a tree of dense systems, maps well to modern memory hierarchies. Furthermore, it promotes the effective use of highly-tuned dense matrix arithmetic kernels, especially on novel and specialized hardware. The graphics processing units (GPUs) are architected differently than general-purpose hosts and offer an order of magnitude more processing power. This paper explores the hypothesis that GPUs can accel-erate the speed of a multifrontal linear solver, even when only processing a small number of the largest frontal matrices. We show that GPUs can more than double the throughput of the sparse matrix factorization. This, in turn, promises to offer a ver...

In this study, an algorithm for computing the inverse of periodic k banded matrices , which are needed for solving the differential equations by using the finite differences, the solution of partial differential equations and the solution of boundary value problems is obtained and the inverses of periodic anti k banded matrices are computed. In addition, the determinant of these type of matrices and the solution of linear systems having these coefficient matrices are investigated. When obtaining this algorithm, the LU factorization is used.The algorithm is implementable to the CAS (Computer Algebra Systems) such as Maple and Mathematica.

A new parallel algorithm for the LU factorization of a given dense matrix A is described. The case of banded matrices is also considered. This algorithm can be combined with Sameh and Brent's [SIAM J. Numer. Anal. 14, 1101Anal. 14, -I 113. (1977))] to obtain the solution of a linear system of algebraic equations. The arithmetic complexity for the dense case is in' ($bn in the banded case), using 3(n -1) processors and no square roots.

In this paper, we compare with the inverse iteration algorithms on PowerXCell T M 8i processor, which has been known as a heterogeneous environment. When some of all the eigenvalues are close together or there are clusters of eigenvalues, reorthogonalization must be adopted to all the eigenvectors associated with such eigenvalues. Reorthogonalization algorithms need a lot of computational cost. The Classical Gram-Schmidt (CGS) algorithm, the modified Gram-Schmidt (MGS) algorithm, and the Householder orthogonalization algorithm in terms of the compact WY representation have been known as reorthogonalization algorithms. These algorithms can be computed using BLAS level-1 and level-2. Since synergistic processor elements in PowerXCell T M 8i processor archive the high performance of BLAS level-2 and level-3, the orthogonalization algorithms except the MGS algorithm can be computed high-speed on parallel computers.

Example with a memory of size 2 data. The graph of input data dependencies is shown on the left. The figure on the right corresponds to the partition and schedule produced by the scheduler ▸ Deque Model Data Aware Ready (DMDAR): Deque Model Data Aware Ready (DMDAR):

In the current article, the authors present a new recursive symbolic computational algorithm, that will never break down, for inverting general periodic pentadiagonal and anti-pentadiagonal matrices. It is a natural generalization of the work presented in [M.E.A. El-Mikkawy, E.D. Rahmo, A new recursive algorithm for inverting general tridiagonal and anti-tridiagonal matrices, Appl. Math. Comput. 204 (2008) 368-372]. The algorithm is suited for implementation using computer algebra systems (CAS) such as Mathematica, Macsyma and Maple. An illustrative example is given.

The Forrest-Tomlin update has stood the test of time within many generations of commercial mathematical programming systems. Its ease of implementation leads to high efficiency and evidently acceptable reliability. We review its relation to Reid's version of the Bartels-Golub update as implemented in LA05, LA15, and LUSOL. In particular, we examine the extent to which FT implementations must "live dangerously" in order to achieve the desired efficiency. Michael Saunders Sparsity vs stability in LU updates 2/31 Bartels-Golub Forrest-Tomlin Sparse BG Two tolerances An experiment Results Conclusion Outline 1 The Bartels-Golub update 2 The Forrest-Tomlin update 3 Sparse Bartels-Golub 4 Two tolerances 5 A numerical experiment 6 Numerical results Bartels-Golub Forrest-Tomlin Sparse BG Two tolerances An experiment Results Conclusion Dense Bartels-Golub

Two unresolved issues regarding dynamic programming,over an inflnite time horizon are addressed within this dissertation. Previous research uses policy improvement to flnd a strong-present-value optimal policy in such systems, but the time complexity of policy improvement is not known. Here, a method is presented for substochastic systems that breaks the problem of flnding a strong-present- value optimal policy into a number of smaller dynamic programming,subproblems. Each of the sub- problems may be solved using linear programming, giving the entire process a polynomial running time with regard to the size of the original dynamic programming problem. Also, for unique transi- tion systems (a specialization of substochastic systems that includes general deterministic systems),

We describe a set of procedures for computing and updating an LU factorization of a sparse matrix A, where A may be square (possibly singular) or rectangular. The procedures include a Markowitz factorization and a Bartels-Golub update, similar to those of Reid (1976, 1982). The updates provided are addition, deletion or replacement of a row or column of A, and rank-one modification. (Previously, column replacement has been the only update available.) Various design features of the implementation (LUSOL) are described, and computational comparisons are made with the LAOS and MAZB packages of Reid (1976) and Duff (1977).

The calculation of overlaps between many-electron wave functions at different nuclear geometries during nonadiabatic dynamics simulations requires the evaluation of a large number of determinants of matrices that differ only in a few rows/columns. While this calculation is fast for small systems, its cost grows faster than the alternative electronic structure calculation used to obtain the wave functions. For wave functions that can be written as a CIS expansion, all determinants can be computed using the set of level-2 minors of the reference matrix. However, this is still a costly computation for large systems. In this paper, we provide an algorithm for efficiently calculating all level-2 minors of a matrix by reutilizing and updating the LU factorization for the determinants of the minors. This approach results in a parallel version of the algorithm that is up to an order of magnitude faster then the current best parallel implementation. The algorithm thus allows the computation of exact wave function overlaps for relatively large systems, with a high density of states, at virtually no cost compared with the electronic structure calculations. Furthermore, the new algorithm opens the path to further investigations in efficient computing of the exact wave function overlaps for complex wave functions such as MR-CIS and MR-CISD.

In this document, we are concerned with the effccts of data layouts for nonsquare processor meshes on the implementation of common dense linear algebra kernels such as matrix-matrix multiplication, LU factorizations, or eigenvalue solvers. In particular, we address ease of programming and tunability of the resulting software. We introduce a generalization of the torus wrap data layout that results in a decoupling of "local" and "global" data layout view. As a result, it allows for intuitive programming of linear algebra algorithms and for tuning of the algorithm for a particular mesh aspect ratio or machine characteristics. This layout is as simple as the proposed HPF layout but, in our opinion, enhances ease of programming as well as ease of performance tuning. We emphasize that we do not advocate that all users need be concerned with these issues. We do, however, believe, that for the foreseeable future "assembler coding" (as message-passing code is likely to be viewed from a HPF programmers' perspective) will be needed to deliver high performance for computationally intensive kernels. As a result, we believe that the adoption of this approach not only would accelerate the generation of efficient linear algebra software libraries but also would accelerate the adoption of HPF as a result. We point out, however, that the adoption of this new layout would necessitate that an HPF compiler ensure that data objects are operated on in a consistent fashion across subroutine and function calls.

This work presents an innovative approach adopted for the development of a new numerical software framework for accelerating dense linear algebra calculations and its application within an engineering context. In particular, response surface models (RSM) are a key tool to reduce the computational effort involved in engineering design processes like design optimization. However, RSMs may prove to be too expensive to be computed when the dimensionality of the system and/or the size of the dataset to be synthesized is significantly high or when a large number of different response surfaces has to be calculated in order to improve the overall accuracy (e.g. like when using ensemble modelling techniques). On the other hand, the potential of modern hybrid hardware (e.g. multicore, GPUs) is not exploited by current engineering tools, while they can lead to a significant performance improvement. To fill this gap, a software framework is being developed that enables the hybrid and scalable a...

Most recent HPC platforms have heterogeneous nodes composed of a combination of multi-core CPUs and accelerators, like GPUs. Scheduling on such architectures relies on a static partitioning and cost model. In this paper, we present a locality-aware work stealing scheduler for multi-CPU and multi-GPU architectures, which relies on the XKaapi runtime system. We show performance results on two dense linear algebra kernels, Cholesky (POTRF) and LU (GETRF) factorization, to evaluate our scheduler on a heterogeneous architecture composed of two hexa-core CPUs and eight NVIDIA Fermi GPUs. Our experiments show that an online locality-aware scheduling achieve performance results as good as static strategies, and in most cases outperform them.

In this paper, we present a comparison of scheduling strategies for heterogeneous multi-CPU and multi-GPU architectures. We designed and evaluated four scheduling strategies on top of XKaapi runtime: work stealing, data-aware work stealing, locality-aware work stealing, and Heterogeneous Earliest-Finish-Time (HEFT). On a heterogeneous architecture with 12 CPUs and 8 GPUs, we analysed our scheduling strategies with four benchmarks: a BLAS-1 AXPY vector operation, a Jacobi 2D iterative computation, and two linear algebra algorithms Cholesky and LU. We conclude that the use of work stealing may be efficient if task annotations are given along with a data locality strategy. Furthermore, our experimental results suggests that HEFT scheduling performs better on applications with very regular computations and low data locality.

The high computational cost involved in modeling of the progressive fracture simulations using large discrete lattice networks stems from the requirement to solve a new large set of linear equations every time a new lattice bond is broken. To address this problem, we propose an algorithm that combines the multiple-rank sparse Cholesky downdating algorithm with the rank-p inverse updating algorithm based on the Sherman-Morrison-Woodbury formula for the simulation of progressive fracture in disordered quasi-brittle materials using discrete lattice networks. Using the present algorithm, the computational complexity of solving the new set of linear equations after breaking a bond reduces to the same order as that of a simple backsolve (forward elimination and backward substitution) using the already LU factored matrix. That is, the computational cost is O(nnz(L)), where nnz(L) denotes the number of non-zeros of the Cholesky factorization L of the stiffness matrix A. This algorithm using the direct sparse solver is faster than the Fourier accelerated preconditioned conjugate gradient (PCG) iterative solvers, and eliminates the critical slowing down associated with the iterative solvers that is especially severe close to the critical points. Numerical results using random resistor networks substantiate the efficiency of the present algorithm.

This special issue of Linear Algebra and its Applications honours Pauline van den Driessche, who celebrates her sixty fifth birthday in 2006. Pauline has made significant contributions to mathematics, especially in linear algebra and mathematical biology. She has been a highly regarded colleague, teacher, collaborator and mentor to many, and a cherished friend to all. We are pleased to congratulate her on this special occasion and to wish her continued success in all future endeavours. Driessche and her contributions to mathematics Pauline van den Driessche was born in 1941 in England and studied mathematics at Imperial College, University of London, where she obtained a B.Sc. and an M.Sc. in applied mathematics. Pauline completed a Ph.D. in fluid mechanics at the University College of Wales in Aberystwyth in 1964. After one year as an Assistant Lecturer at the University College of Wales, she emigrated to Canada with her husband, Robert, and joined the Department of Mathematics at the University of Victoria in 1965. She has since lived in Victoria, apart from study leaves spent in Australia, Toronto, Oxford, Munich, Bielefeld and Edmonton, and several research visits, especially to other universities in Canada. Her supportive family, which brings her great joy, includes a son Mark and a daughter Ruth, and three grandsons. Pauline is an internationally renowned scientist who has made significant contributions in several different areas of mathematics. Her solid grounding in applied mathematics laid a foundation for her work in dynamical systems and applications. Her earlier work on differential-difference equations and Hopf bifurcations is widely known, and is still cited in the literature, a tribute to the lasting impact of her work. Pauline is well known and internationally recognized for the depth and breadth of her work in linear algebra. She was among the earliest researchers in combinatorial matrix analysis, in which the zero-nonzero or sign pattern of a matrix is exploited in analyzing such matrix properties as stability, nonsingularity, inertia and the

A class of matrices that simultaneously generalizes the M-matrices and the inverse M-matrices is brought forward and its properties are reviewed. It is interesting to see how this class bridges the properties of the matrices it generalizes and provides a new perspective on their classical theory.

Calculating the log-determinant of a matrix is useful for statistical computations used in machine learning, such as generative learning which uses the log-determinant of the covariance matrix to calculate the log-likelihood of model mixtures. The log-determinant calculation becomes challenging as the number of variables becomes large. Therefore, finding a practical speedup for this computation can be useful. In this study, we present a parallel matrix condensation algorithm for calculating the log-determinant of a large matrix. We demonstrate that in a distributed environment, Parallel Matrix Condensation has several advantages over the well-known Parallel Gaussian Elimination. The advantages include high data distribution efficiency and less data communication operations. We test our Parallel Matrix Condensation against self-implemented Parallel Gaussian Elimination as well as ScaLAPACK (Scalable Linear Algebra Package) on 1000 x1000 to 8000x8000 for 1,2,4,8,16,32,64 and 128 processors. The results show that Matrix Condensation yields the best speed-up among all other tested algorithms. The code is available on

This paper extends the ideas behind Bareiss's fraction-free Gauss elimination algorithm in a number of directions. First, in the realm of linear algebra, algorithms are presented for fraction-free LU "factorization" of a matrix and for fraction-free algorithms for both forward and back substitution. These algorithms are valid not just for integer computation but also for any matrix system where the entries are taken from a unique factorization domain such as a polynomial ring. The second part of the paper introduces the application of the fraction-free formulation to resultant algorithms for solving systems of polynomial equations. In particular, the use of fraction-free polynomial arithmetic and triangularization algorithms in computing the Dixon resultant of a polynomial system is discussed.

Steganography is one of the most important tools in the data security field as there is a huge amount of data transferred each moment over the internet. Hiding secret messages in an image has been widely used because the images are mostly used in social media applications. The proposed algorithm is a simple algorithm for hiding an image in another image. The proposed technique uses QR factorization to conceal the secret image. The technique successfully hid a gray and color image in another one and the performance of the algorithm was measured by PSNR, SSIM and NCC. The PSNR for the cover image was in the range of 41 to 51 dB. DWT was added to increase the security of the method and this enhanced technique increased the cover PSNR to 48 t0 56 dB. The SSIM is 100% and the NCC is 1 for both implementations. Which improves that the imperceptibility of the algorithm is very high. The comparative analysis showed that the performance of the algorithm is better than other state-of-the-art ...

In this work an architecture of an automatically tuned linear algebra library proposed in previous works is extended in order to adapt it to platforms where both the CPU load and the network traffic vary. During the installation process in a system, the linear algebra routines will be tuned automatically to the system conditions: hardware characteristics and basic libraries used in the linear algebra routines. At run-time the parameters that define the system characteristics are adjusted to the actual load of the platform. The design methodology is analysed with a block LU factorisation. Variants for a sequential and parallel version of this routine on a logical rectangular mesh of processors are considered. The behaviour of the algorithm is studied with message-passing, using MPI on a cluster of PCs. The experiments show that the configurable parameters of the linear algebra routines can be adjusted during the run-time process despite the variability of the environment.

We study the impact of non-uniform memory accesses (NUMA) on the solution of dense general linear systems using an LU factorization algorithm. In particular we illustrate how an appropriate placement of the threads and memory on a NUMA architecture can improve the performance of the panel factorization and consequently accelerate the global LU factorization. We apply these placement strategies and present performance results for a hybrid multicore/GPU LU algorithm as it is implemented in the public domain library MAGMA.

In this paper we study properties of definite quadratic eigenproblems. Free vibrations of fluid-solid structures are governed by a nonsymmetric eigenvalue problem. This problem can be transformed into a definite quadratic eigenvalue problem. Niendorf and Voss presented an algorithm which determents if quadratic pencil is or is not definite. In their algorithm, the initial vector is taken at random. In this paper we bring a new effective algorithm for determining the initial vector x0 and thus we accelerate algorithm of Niendorf and Voss. The new algorithm presented in this paper combines earlier results of Kostic and Sikalo with the new results obtained in this study.

In this paper, we describe a reliable symbolic computational algorithm for inverting general cyclic heptadiagonal matrices by using parallel computing along with recursion. The algorithm is implementable to the Computer Algebra System(CAS) such as MAPLE, Matlab and Mathematica . An example is presented for the sake of illustration.

Das Tondo Die Anbetung der hl. drei Könige, heute in der Gemäldegalerie in Berlin, wird Domenico Veneziano zugeschrieben. Im Vordergrund bezeugt eine Gruppe herrschaftlicher Menschen in prächtigen Gewändern, unter ihnen die drei Könige, dem Kind ihre Ehrerbietung. Der älteste König kniet langgestreckt auf dem Boden und küsst ihm die Füße. Die Gruppe setzt sich, einschließlich Maria und Josef, aus vorwiegend männlichen Würdenträgern zusammen. Ein Würdenträger in einem weißen Faltengewand hält einen Vogel mit rotem Schopf, wohl einen Auerhahn, auf dem Arm. Davon abgesetzt baut sich die Gruppe der Reiter auf, die, angeregt durch einen Reiter in einem schwarzen Pollunder, ebenfalls auf das Geschehen bezogen ist. Allerlei Getier, u.a. zwei Hunde und neu geschlüpfte Vögel sowie Fauna säumen die rituelle Handlung. Eine mächtige Tanne gibt den Blick auf eine Schafherde und eine burgähnliche Anlage frei. Linkerhand lassen sich weitere Wehrtürme ausmachen. Auf den Wegen sind Menschen unterwegs, die zum Kind pilgern. Das Tal liegt weitgehend im Schatten, nur eine höher gelegene Kuppe wird noch von der Sonne beschienen. Ein hellblauer, kaum bewölkter Himmel geht am Horizont in gleißendes Weiß über. Überhaupt nimmt die Natur einen breiten Raum in dem Rundbild ein.

Das Tondo Die Anbetung der hl. drei Könige, heute in der Gemäldegalerie in Berlin, wird Domenico Veneziano zugeschrieben. Im Vordergrund bezeugt eine Gruppe herrschaftlicher Menschen in prächtigen Gewändern, unter ihnen die drei Könige, dem Kind ihre Ehrerbietung. Der älteste König kniet langgestreckt auf dem Boden und küsst ihm die Füße. Die Gruppe setzt sich, einschließlich Maria und Josef, aus vorwiegend männlichen Würdenträgern zusammen. Ein Würdenträger in einem weißen Faltengewand hält einen Vogel mit rotem Schopf, wohl einen Auerhahn, auf dem Arm. Davon abgesetzt baut sich die Gruppe der Reiter auf, die, angeregt durch einen Reiter in einem schwarzen Pollunder, ebenfalls auf das Geschehen bezogen ist. Allerlei Getier, u.a. zwei Hunde und neu geschlüpfte Vögel sowie Fauna säumen die rituelle Handlung. Eine mächtige Tanne gibt den Blick auf eine Schafherde und eine burgähnliche Anlage frei. Linkerhand lassen sich weitere Wehrtürme ausmachen. Auf den Wegen sind Menschen unterweg...

Maurice Potron (1872-1942) is a French Jesuit and mathematician whose main source of inspiration in economics is the encyclical Rerum Novarum. With virtually no knowledge in economic theory, he wrote down a linear model of production in which he formalized the notions of just prices and just wages. As early as 1911, he used the Perron-Frobenius theorem to prove the existence of a positive solution and established a duality result between the quantity side and the price side of the model. He returned to economics in the 1930s, but in both periods he failed to make a lasting impression upon economists.

One wishes to remove k − 1 edges of a vertex-weighted tree T such that the weights of the k induced connected components are approximately the same. How well can one do it ? In this paper, we investigate such k-separator for quasi-binary trees. We show that, under certain conditions on the total weight of the tree, a particular k-separator can be constructed such that the smallest (respectively the largest) weighted component is lower (respectively upper) bounded. Examples showing optimality for the lower bound are also given.

We consider the finite element environment Getfem++ 1 , which is a C++ library of generic finite element functionalities and allows for parallel distributed data manipulation and assembly. For the solution of the large sparse linear systems arising from the finite element assembly, we consider the multifrontal massively parallel solver package Mumps 2 , which implements a parallel distributed LU factorization of large sparse matrices. In this work, we present the integration of the Mumps package into Getfem++ that provides a complete and generic parallel distributed chain from the finite element discretization to the solution of the PDE problems. We consider the parallel simulation of the transition to turbulence of a flow around a circular cylinder using Navier Stokes equations, where the nonlinear term is semi-implicit and requires that some of the discretized differential operators be updated and with an assembly process at each time step. The preliminary parallel experiments using this new combination of Getfem++ and Mumps are presented.

Solving linear systems is a fundamental task in several areas of mathematics and engineering, playing a crucial role in solving real-world problems. MATLAB, a powerful numerical computing platform, offers a wide range of tools and resources to efficiently address this type of problem. For the purposes of this article, we will explore how MATLAB can be used to solve linear systems. Additionally, MATLAB offers the ability to work with matrices, making it particularly suitable for dealing with systems of linear equations represented in this form. Through practical examples, we will illustrate how to use MATLAB functionalities to solve linear systems of different sizes and complexities. Finally, we will highlight the advantages of using MATLAB to solve linear systems, including its computational efficiency, ability to deal with large and complex systems, and the ease of visualizing results, making it a great tool to help students in their studies and research.

This work deals with the numerical solution of systems of oscillatory second-order differential equations which often arise from the semi-discretization in space of partial differential equations. Since these differential equations exhibit (pronounced or highly) oscillatory behavior, standard numerical methods are known to perform poorly. Our approach consists in directly discretizing the problem by means of Gautschi-type integrators based on sinc matrix functions. The novelty contained here is that of using a suitable rational approximation formula for the sinc matrix function to apply a rational Krylov-like approximation method with suitable choices of poles. In particular, we discuss the application of the whole strategy to a finite element discretization of the wave equation.

Subspace channel estimation methods have been<br> studied widely, where the subspace of the covariance matrix is<br> decomposed to separate the signal subspace from noise subspace. The<br> decomposition is normally done by using either the eigenvalue<br> decomposition (EVD) or the singular value decomposition (SVD) of<br> the auto-correlation matrix (ACM). However, the subspace<br> decomposition process is computationally expensive. This paper<br> considers the estimation of the multipath slow frequency hopping<br> (FH) channel using noise space based method. In particular, an<br> efficient method is proposed to estimate the multipath time delays by<br> applying multiple signal classification (MUSIC) algorithm which is<br> based on the null space extracted by the rank revealing LU (RRLU)<br> factorization. As a result, precise information is provided by the<br> RRLU about the numerical null space and the r...

Linear feature space transformations are often used for speaker or environment adaptation. Usually, numerical methods are sought to obtain solutions. In this paper, we derive a closed-form solution to ML estimation of full feature transformations. Closed-form solutions are desirable because the problem is quadratic and thus blind numerical analysis may be lured into the recess of numerically valid, albeit poor, attractors. We decompose the transformation into upper and lower triangular matrices, which are estimated alternatively using the EM algorithm. Furthermore, we extend the theory to Bayesian adaptation. On the Switchboard task, we obtain 1.6% WER improvement by combining the method with MLLR, or 4% absolute using adaptation.

The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that: • a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.

Parallel loops are an important part of OpenMP programs. Efficient scheduling of parallel loops can improve performance of the programs. The current OpenMP specification only offers three options for loop scheduling, which are insufficient in certain instances. Given the large number of other possible scheduling strategies, standardizing each of them is infeasible. A more viable approach is to extend the OpenMP standard to allow a user to define loop scheduling strategies within her application. The approach will enable standard-compliant application-specific scheduling. This work analyzes the principal components required by user-defined scheduling and proposes two competing interfaces as candidates for the OpenMP standard. We conceptually compare the two proposed interfaces with respect to the three host languages of OpenMP, i.e., C, C++, and Fortran. These interfaces serve the OpenMP community as a basis for discussion and prototype implementation supporting user-defined scheduling in an OpenMP library.

Parallel loops are an important part of OpenMP programs. Efficient scheduling of parallel loops can improve performance of the programs. The current OpenMP specification only offers three options for loop scheduling, which are insufficient in certain instances. Given the large number of other possible scheduling strategies, standardizing each of them is infeasible. A more viable approach is to extend the OpenMP standard to allow a user to define loop scheduling strategies within her application. The approach will enable standard-compliant application-specific scheduling. This work analyzes the principal components required by user-defined scheduling and proposes two competing interfaces as candidates for the OpenMP standard. We conceptually compare the two proposed interfaces with respect to the three host languages of OpenMP, i.e., C, C++, and Fortran. These interfaces serve the OpenMP community as a basis for discussion and prototype implementation supporting user-defined scheduling in an OpenMP library.

A nonsingular real matrix A is said to be inverse-positive if all the elements of its inverse are nonnegative. This class of matrices contains the M-matrices, from which inherit some of their properties and applications, especially in Economy. In this work we analyze the inverse-positive concept for a particular type of pattern: the checkerboard pattern. In addition, we study the Hadamard product of certain classes of inverse-positive matrices whose entries have a particular sign pattern.

A nonsingular real matrix A is said to be inverse-positive if all the elements of its inverse are nonnegative. This class of matrices contains the M-matrices, from which inherit some of their properties and applications, especially in Economy. In this work we analyze the inverse-positive concept for a particular type of pattern: the checkerboard pattern. In addition, we study the Hadamard product of certain classes of inverse-positive matrices whose entries have a particular sign pattern.

In this work an architecture of an automatically tuned linear algebra library proposed in previous works is extended in order to adapt it to platforms where both the CPU load and the network traffic vary. During the installation process in a system, the linear algebra routines will be tuned automatically to the system conditions: hardware characteristics and basic libraries used in the linear algebra routines. At run-time the parameters that define the system characteristics are adjusted to the actual load of the platform. The design methodology is analysed with a block LU factorisation. Variants for a sequential and parallel version of this routine on a logical rectangular mesh of processors are considered. The behaviour of the algorithm is studied with message-passing, using MPI on a cluster of PCs. The experiments show that the configurable parameters of the linear algebra routines can be adjusted during the run-time process despite the variability of the environment.

In this work, we consider the problem of calculating the generalized Moore–Penrose inverse, which is essential in many applications of graph theory. We propose an algorithm for the massively parallel systems based on the recursive algorithm for the generalized Moore–Penrose inverse, the generalized Cholesky factorization, and Strassen’s matrix inversion algorithm. Computational experiments with our new algorithm based on a parallel computing architecture known as the Compute Unified Device Architecture (CUDA) on a graphic processing unit (GPU) show the significant advantages of using GPU for large matrices (with millions of elements) in comparison with the CPU implementation from the OpenCV library (Intel, Santa Clara, CA, USA).

We address the parallelization of the LU factorization of hierarchical matrices (H-matrices) arising from boundary element methods. Our approach exploits task-parallelism via the OmpSs programming model and runtime, which discovers the data-flow parallelism intrinsic to the operation at execution time, via the analysis of data dependencies based on the memory addresses of the tasks' operands. This is especially challenging for H-matrices, as the structures containing the data vary in dimension during the execution. We tackle this issue by decoupling the data structure from that used to detect dependencies. Furthermore, we leverage the support for weak operands and early release of dependencies, recently introduced in OmpSs-2, to accelerate the execution of parallel codes with nested task-parallelism and fine-grain tasks.

We present a prototype task-parallel algorithm for the solution of hierarchical symmetric positive definite linear systems via the ℋ-Cholesky factorization that builds upon the parallel programming standards and associated runtimes for OpenMP and OmpSs. In contrast with previous efforts, our proposal decouples the numerical aspects of the linear algebra operation from the complexities associated with high performance computing. Our experiments make an exhaustive analysis of the efficiency attained by different parallelization approaches that exploit either task-parallelism or loop-parallelism via a runtime. Alternatively, we also evaluate a solution that leverages multi-threaded parallelism via the parallel implementation of the Basic Linear Algebra Subroutines (BLAS) in Intel MKL.

We propose two novel techniques for overcoming load-imbalance encountered when implementing so-called look-ahead mechanisms in relevant dense matrix factorizations for the solution of linear systems. Both techniques target the scenario where two thread teams are created/activated during the factorization, with each team in charge of performing an independent task/branch of execution. The first technique promotes worker sharing (WS) between the two tasks, allowing the threads of the task that completes first to be reallocated for use by the costlier task. The second technique allows a fast task to alert the slower task of completion, enforcing the early termination (ET) of the second task, and a smooth transition of the factorization procedure into the next iteration. The two mechanisms are instantiated via a new malleable thread-level implementation of the Basic Linear Algebra Subprograms (BLAS), and their benefits are illustrated via an implementation of the LU factorization with partial pivoting enhanced with look-ahead. Concretely, our experimental results on a six core Intel-Xeon processor show the benefits of combining WS+ET, reporting competitive performance in comparison with a taskparallel runtime-based solution.