Matrix Decomposition Algorithms Related to the MFS for Axisymmetric Problems

2009 ◽  
pp. 223-237 ◽  
Author(s):  
Andreas Karageorghis ◽  
Yiorgos–Sokratis Smyrlis
Keyword(s):  
Matrix Decomposition ◽  
Decomposition Algorithms ◽  
Matrix Decomposition Algorithms ◽  
Axisymmetric Problems

scholarly journals Parallel real-world LU decomposition: Gauss vs. Crout algorithm

2018 ◽  
Vol 8 (1) ◽  
pp. 210-217
Author(s):  
Marek Stabrowski
Keyword(s):  
Real World ◽  
Numerical Experiments ◽  
Matrix Decomposition ◽  
Decomposition Algorithms ◽  
Density Matrices ◽  
Hardware Platform ◽  
Posix Threads ◽  
Real World Applications ◽  
Matrix Decomposition Algorithms ◽  
Algorithm Implementation

Abstract This paper presents numerical experiments with assorted versions of parallel LU matrix decomposition algorithms (Gauss and Crout algorithm). The tests have been carried out on the hardware platform with fourcore Skylake processor featuring hyperthreading technology doubling virtually core number. Parallelization algorithms have been implemented with the aid of classic POSIX threads library. Experiments have shown that basic 4-thread acceleration of all parallel implementations is almost equal to the number of threads/processors. Both algorithms are worth considering in real-world applications (Florida University collection). Gauss algorithm is a better performer, with respect to timing, in the case of matrices with lower density of nonzeros, as opposed to higher density matrices. The latter are processed more efficiently with the aid of Crout algorithm implementation.

Matrix decomposition algorithms for the finite element Galerkin method with piecewise Hermite cubics

2008 ◽  
Vol 52 (1) ◽  
pp. 1-23 ◽  
Author(s):  
Bernard Bialecki ◽  
Graeme Fairweather ◽  
David B. Knudson ◽  
D. Abram Lipman ◽  
Que N. Nguyen ◽  
...  
Keyword(s):  
Finite Element ◽  
Galerkin Method ◽  
Matrix Decomposition ◽  
Decomposition Algorithms ◽  
Finite Element Galerkin Method ◽  
Matrix Decomposition Algorithms ◽  
Piecewise Hermite Cubics

Application of matrix decomposition algorithms for singular matrices to the Pawley method inZ-Rietveld

2012 ◽  
Vol 45 (2) ◽  
pp. 299-308 ◽  
Author(s):  
R. Oishi-Tomiyasu ◽  
M. Yonemura ◽  
T. Morishima ◽  
A. Hoshikawa ◽  
S. Torii ◽  
...  
Keyword(s):  
Matrix Decomposition ◽  
Nonlinear Least Squares ◽  
Rietveld Analysis ◽  
Linear Constraints ◽  
Proton Accelerator ◽  
Decomposition Algorithms ◽  
New Approach ◽  
Matrix Decomposition Algorithms ◽  
Singular Matrices ◽  
Integrated Intensities

Z-Rietveldis a program suite for Rietveld analysis and the Pawley method; it was developed for analyses of powder diffraction data in the Materials and Life Science Facility of the Japan Proton Accelerator Research Complex. Improvements have been made to the nonlinear least-squares algorithms ofZ-Rietveldso that it can deal with singular matrices and intensity non-negativity constraints. Owing to these improvements,Z-Rietveldsuccessfully executes the Pawley method without requiring any constraints on the integrated intensities, even in the case of severely or exactly overlapping peaks. In this paper, details of these improvements are presented and their advantages discussed. A new approach to estimate the number of independent reflections contained in a powder pattern is introduced, and the concept of good reflections proposed by Sivia [J. Appl. Cryst.(2000),33, 1295–1301] is shown to be explained by the presence of intensity non-negativity constraints, not the intensity linear constraints.

Matrix Decomposition Algorithms for Modified Spline Collocation for Helmholtz Problems

2003 ◽  
Vol 24 (5) ◽  
pp. 1733-1753 ◽  
Author(s):  
Bernard Bialecki ◽  
Graeme Fairweather ◽  
Andreas Karageorghis
Keyword(s):  
Matrix Decomposition ◽  
Decomposition Algorithms ◽  
Spline Collocation ◽  
Matrix Decomposition Algorithms
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