Mathematics of Scientific Computing

This article presents one modification of algorithm for generation of n-dimensional rotation matrix M, which rotates given n-dimensional vector X to the direction of given n-dimensional vector Y. Algorithm, named N-dimensional Rotation Matrix Generation Algorithm (NRMG) includes rotations of given vectors X and Y to the direction of coordinate axis x1 using twodimensional rotations in coordinate planes. Proposed modification decreases the number of needed twodimensional rotations to 2(Lw-1) were Lw is the number of corresponding components of the two given vectors, that are not equal.

This article presents a new algorithm for generation of N-dimensional rotation matrix M, which rotates given N-dimensional vector X to the direction of given vector Y which has the same dimension. Algorithm, named N-dimensional Rotation Matrix Generation Algorithm (NRMG) includes rotation of given vectors X and Y to the direction of coordinate axis x 1 using two-dimensional rotations. Matrix M is obtained as multiplication of matrix M X and inverse of matrix M Y , which rotates given vectors to the direction of axis x 1. Also examined is the possibility to perform parallel calculations of two-dimensional rotations.

Of concern in this work is the derivation and implementation of the multistep methods through Taylor's expansion and numerical integration. For the Taylor's expansion method, the series is truncated after some terms to give the needed approximations which allows for the necessary substitutions for the derivatives to be evaluated on the differential equations. For the numerical integration technique, an interpolating polyn omial that is determined by some data points replaces the differential equation function and it is integrated over a specified interval. The methods show that they are only convergent if and only if they are consistent and stable. In our numerical example s, the methods are applied on non-stiff initial value problems of first-order ordinary differential equations, where it is established that the multistep methods show superiority over the single-step methods in terms of robustness, efficiency, stability and accuracy, the only setback being that the multistep methods require more computational effort than the single-step methods.

This article proposes an algorithm for generation of N-dimensional rotation matrix R, N=m+n, m=2 p , n=2 q , p,q  [2, 4, 8] which rotates given N-dimensional vector X in the direction of coordinate axis x1 Algorithm uses block diagonal matrix, composed by Transpositions matrices. As practical realization article gives Matlab code of functions, which creates Householder and Transpositions matrices and V matrix for given n-dimensional vector X.

In this paper, we provide the solution of a modeled parallel resonant circuit using the decomposition method. The parallel resonant circuit also known as resistor (R) in ohms, inductor (L) in Henry and capacitor (C) in farads (RLC) circuit is used in turning radio or audio receivers. The mathematical models are in a system of ordinary differential equations (ODE), which we solve using the Adomian Decomposition Method (ADM). We discovered that this method gave exact solutions as can be obtained using any traditionally known analytic method. These findings are illustrated in three test problems.

This article presents one modification of algorithm for generation of n-dimensional rotation matrix M, which rotates given n-dimensional vector X to the direction of given n-dimensional vector Y. Algorithm, named N-dimensional Rotation Matrix Generation Algorithm (NRMG) includes rotations of given vectors X and Y to the direction of coordinate axis x1 using twodimensional rotations in coordinate planes. Proposed modification decreases the number of needed twodimensional rotations to 2(Lw-1) were Lw is the number of corresponding components of the two given vectors, that are not equal.

In this paper, we describe the methodology and the results of the statistical analysis, data mining, graph analysis and network analytics of cinematography data retrieved from the Linked Open Data cloud. The entire dataset was extracted with SPARQL queries, cleaned with Open Refine, and imported to R for data analysis. The methods applied were Cross Correlation, Mutual Information and Granger Causality. The results are visualized through an application that was created using R language’s library ”shinydashboard”, giving the user the opportunity to view and edit the results with a set of widgets. This paper is a study that demonstrates the benefits of using Linked Open Data in Data Science and its methodology can be reused in many other multivariate Linked Open Data subjects. CCS Concepts •Mathematics of computing → Time series analysis; Graph theory; •Information systems → Data mining; Data cleaning; •Applied computing → Mathematics and statistics; •Theory of computation → Data inte...

In this paper, we present new iterative algorithms to find a root of the given nonlinear transcendental equations. In the proposed algorithms, we use nonlinear Taylor’s polynomial interpolation and a modified error correction term with a fixed-point concept. We also investigated for possible extension of the higher order iterative algorithms in single variable to higher dimension. Several numerical examples are presented to illustrate the proposed algorithms.

— This article presents one modification of algorithm for generation of n-dimensional rotation matrix M, which rotates given n-dimensional vector X to the direction of given n-dimensional vector Y. Algorithm, named N-dimensional Rotation Matrix Generation Algorithm (NRMG) includes rotations of given vectors X and Y to the direction of coordinate axis x1 using two-dimensional rotations in coordinate planes. Proposed modification decreases the number of needed two-dimensional rotations to 2(Lw-1) were Lw is the number of corresponding components of the two given vectors, that are not equal.

This article presents one modification of algorithm for generation of n-dimensional rotation matrix M, which rotates given n-dimensional vector X to the direction of given n-dimensional vector Y. Algorithm, named N-dimensional Rotation Matrix Generation Algorithm (NRMG) includes rotations of given vectors X and Y to the direction of coordinate axis x1 using two-dimensional rotations in coordinate planes. Proposed modification decreases the number of needed two-dimensional rotations to 2(Lw-1) were Lw is the number of corresponding components of the two given vectors, that are not equal.

In this paper, we describe the methodology and the results of the statistical analysis, data mining, graph analysis and network analytics of cinematography data retrieved from the Linked Open Data cloud. The entire dataset was extracted with SPARQL queries, cleaned with Open Refine, and imported to R for data analysis. The methods applied were Cross Correlation, Mutual Information and Granger Causality. The results are visualized through an application that was created using R language's library " shinydash-board " , giving the user the opportunity to view and edit the results with a set of widgets. This paper is a study that demonstrates the benefits of using Linked Open Data in Data Science and its methodology can be reused in many other multivariate Linked Open Data subjects.