Conference Presentations by D. Bertaccini
The efficient numerical solution of the large linear systems of partial fractional differential e... more The efficient numerical solution of the large linear systems of partial fractional differential equations is considered here. The key tool used is the short-memory principle. The latter ensures the decay of the entries of the inverse of the discretized operator, whose inverses are approximated by a sequence of sparse matrices. On this ground, we propose to solve the underlying linear systems directly by these approximations or by iterative solvers using sequence of preconditioners based on the above mentioned inverses.
A strategy for updating preconditioner for solving a succession of linear system with Iterative K... more A strategy for updating preconditioner for solving a succession of linear system with Iterative Krylov Solvers. Presentation of the results for the case of symmetric matrices sequences and preliminary results for the case of non symmetric and non definite matrices.
Papers by D. Bertaccini
Distortion products and backward-traveling waves in nonlinear active models of the cochlea
This study explores the phenomenology of distortion products in nonlinear cochlear models, predic... more This study explores the phenomenology of distortion products in nonlinear cochlear models, predicting their amplitude and phase along the basilar membrane. The existence of a backward-traveling wave at the distortion-product frequency, which has been recently questioned by experiments measuring the phase of basilar-membrane vibration, is discussed. The effect of different modeling choices is analyzed, including feed-forward asymmetry, micromechanical roughness, and breaking of scaling symmetry. The experimentally observed negative slope of basilar-membrane phase is predicted by numerical simulations of nonlinear cochlear models under a wide range of parameters and modeling choices. In active models, positive phase slopes are predicted by the quasi-linear analytical computations and by the fully nonlinear numerical simulations only if the distortion-product sources are localized apical to the observation point and if the stapes reflectivity is unrealistically small. The results of this study predict a negative phase slope whenever the source is distributed over a reasonably wide cochlear region and/or a reasonably high stapes reflectivity is assumed. Therefore, the above-mentioned experiments do not contradict "classical" models of cochlear mechanics and of distortion-product generation.
SIAM Journal on Matrix Analysis and Applications, 2007
The convergence features of a preconditioned algorithm for the convection-diffusion equation base... more The convergence features of a preconditioned algorithm for the convection-diffusion equation based on its diffusion part are considered. Analyses of the distribution of the eigenvalues of the preconditioned matrix in arbitrary dimensions and of the fundamental parameters of convergence are provided, showing the existence of a proper cluster of eigenvalues. The structure of the cluster is not influenced by the discretization. An upper bound on the condition number of the eigenvector matrix under some assumptions is provided as well. The overall cost of the algorithm is O(n), where n is the size of the underlying matrices.
Numerische Mathematik, 2005
We study the role of preconditioning strategies recently developed for coercive problems in conne... more We study the role of preconditioning strategies recently developed for coercive problems in connection with a two-step iterative method, based on the Hermitian skew-Hermitian splitting (HSS) of the coefficient matrix, proposed by Bai, Golub and Ng for the solution of nonsymmetric linear systems whose real part is coercive. As a model problem we consider Finite Differences (FD) matrix sequences {A n (a, p)} n discretizing the elliptic
Numerical schemes for pricing of multidimensional options with jumps
BOOK OF …, 2006
[1], fail to keep the monotonicity properties. An asymmetric scheme, fully implicit in the differ... more [1], fail to keep the monotonicity properties. An asymmetric scheme, fully implicit in the differential part and explicit in the integral term, has been investigated in [4], still using the framework of viscosity solutions. This scheme is unconditionally stable, but to keep a good accuracy of ...
Un Modello Nonlineare Nonlocale Della Coclea
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La coclea e'un sistema intrinsecamente non lineare, e caratterizzato da due aspetti compleme... more La coclea e'un sistema intrinsecamente non lineare, e caratterizzato da due aspetti complementari fra loro: propagazione di onde viaggianti (TW) lungo la membrana basilare (BM) e nel fluido, e risonanza tonotopica di ogni componente frequenziale della TW in un ...
E卤cient preconditioning for sequences of parametric complex symmetric linear systems
Abstract. Solution of sequences of complex symmetric linear systems of the form Ajxj = bj, j = 0;... more Abstract. Solution of sequences of complex symmetric linear systems of the form Ajxj = bj, j = 0; :::; s, Aj = A + jEj, A Hermitian, E0; :::; Es complex diagonal matrices and 0; :::; s scalar complex parameters arise in a variety of challenging problems. This is the case of time dependent PDEs; lattice gauge computations in quantum
P-circulant preconditioners and the systems of ODE codes
A Flexible Updating Framework for Preconditioners in PDE-Based Image Restoration Algorithms
Numerical Mathematics and Advanced Applications 2009, 2010
An Adaptive Norm Algorithm for Image Restoration
Lecture Notes in Computer Science, 2012
Skew-Circulant Preconditioners for Systems of LMF-Based ODE Codes
Lecture Notes in Computer Science, 2001
We consider the solution of ordinary differential equations (ODEs) using implicit linear multiste... more We consider the solution of ordinary differential equations (ODEs) using implicit linear multistep formulae (LMF). More precisely, here we consider Boundary Value Methods. These methods require the solution of one or more unsymmetric, large and sparse linear systems. In [6], Chan et al. proposed using Strang block-circulant preconditioners for solving these linear systems. However, as observed in [1], Strang preconditioners can be often ill-conditioned or singular even when the given system is well-conditioned. In this paper, we propose a nonsingular skew-circulant preconditioner for systems of LMF-based ODE codes. Numerical results are given to illustrate the effectiveness of our method.
Spectral Analysis and Superlinear Convergence of a Preconditioned Iterative Method for the Convection-Diffusion Equation
Numerical simulations of the Transient-evoked Otoacoustic response
Approximate Inverse Preconditioners for Krylov Methods on Heterogeneous Parallel Computers
Analysis of a preconditioned iterative method for the convection-diffusion equation
Quasi matrix free preconditioners in optimization and nonlinear least-squares
The approximate solution of several nonlinear optimization problems requires solving sequences of... more The approximate solution of several nonlinear optimization problems requires solving sequences of symmetric linear systems. When the number of variables is large, it is advisable to use an iterative linear solver for the Newton correction step. On the other hand, the underlying linear solver can converge slowly and the calculation of a preconditioner requires the computation of the Hessian matrix
Numerical Simulations of Otoacoustic Emissions from a Non-linear Non-local Cochlear Model
Otoacoustic emissions are numerically simulated from a nonlinear nonlocal cochlear model solved i... more Otoacoustic emissions are numerically simulated from a nonlinear nonlocal cochlear model solved in time domain by means of the space-state matrix technique. The feedback mechanism localized in the outer hair cells system is modeled as a nonlinear active force proportional to the total pressure acting on the basilar membrane or as an anti-damping nonlinear term proportional to the velocity of
Preconditioned HSS method for the solution of non-Hermitian positive definite linear systems
Abstract: We study the role of preconditioning strategies recently developed for coercive problem... more Abstract: We study the role of preconditioning strategies recently developed for coercive problems in connectionwith a two-step iterative method (HSS) proposed by Bai, Golub and Ng for the solution of nonsymmetriclinear systems whose real part is coercive. As a model problem we consider Finite Dierences (FD) matrixsequences fAn(a; p)gn discretizing the elliptic (convection-diusion) problemAa;pu r[a(x)ru(x)] +r[p(x)u(x)] = f(x); xDirichlet BC;(1)withwith a(x) being a uniformly...
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Conference Presentations by D. Bertaccini
Papers by D. Bertaccini