High Performance Portable Solver for Tridiagonal Toeplitz Systems of Linear Equations

2021 ◽  
pp. 172-184
Author(s):  
Beata Dmitruk ◽  
Przemysław Stpiczyński
Keyword(s):  
High Performance ◽  
Linear Equations ◽  
Systems Of Linear Equations ◽  
Toeplitz Systems

A Superfast Algorithm for Toeplitz Systems of Linear Equations

2008 ◽  
Vol 29 (4) ◽  
pp. 1247-1266 ◽  
Author(s):  
S. Chandrasekaran ◽  
M. Gu ◽  
X. Sun ◽  
J. Xia ◽  
J. Zhu
Keyword(s):  
Linear Equations ◽  
Systems Of Linear Equations ◽  
Toeplitz Systems ◽  
Superfast Algorithm

Evaluation of Different Approaches to Solution of the Direct Solution of Large, Sparse Systems of Linear Equations

2017 ◽  
Vol 1144 ◽  
pp. 97-101
Author(s):  
Michal Bošanský ◽  
Bořek Patzák
Keyword(s):  
High Performance ◽  
Linear Equations ◽  
Object Oriented ◽  
General Purpose ◽  
Finite Element Code ◽  
Direct Solution ◽  
Iterative Solver ◽  
Systems Of Linear Equations ◽  
Sparse Systems ◽  
Symmetric Systems

The aim of this paper is to the evaluate efficiency of differentapproaches to solution of large, sparse, non-symmetric systems of linearequations on high performance machines, that can be found in any finiteelement software. The different approaches based on direct or iterativealgorithms for solution of linear equations are compared. In particular,directs solver using Skyline sparse storage, direct solver from SuperLUlibrary, iterative solver from Iterative Method Library(IML)are compared. SuperLU is a general purpose library for the directsolution of large, sparse, nonsymmetric systems of linear equations.Additionally, the performance and scalability of parallel SuperLU solveris studied, based on OpenMP. The paper shows thatparallelization can efficiently exploit the power of modern availablehardware, significantly reducing the needed computation time.The different strategies were implemented in OOFEM which is afree finite element code with object oriented architecture for solvingmechanical, transport and fluid mechanics problems that operates onvarious platforms.

An Improved Fast Algorithm for Solving Toeplitz Systems in Mechanical Control

2011 ◽  
Vol 55-57 ◽  
pp. 863-867
Author(s):  
Li Chao Tian ◽  
Hong Kui Li
Keyword(s):  
Fast Algorithm ◽  
Toeplitz Matrices ◽  
Linear Equations ◽  
Mechanical Control ◽  
Systems Of Linear Equations ◽  
Toeplitz Systems

Pentadiagonal Toeplitz systems of linear equations arise in many application areas. Because of the structure and many good properties of pentadiagonal Toeplitz matrices, they have been applied in Mechanical Control. Based on [1], in this paper, we present an improved fast algorithm for solving symmetric pentadiagonal Toeplitz systems.

scholarly journals Accelerated Circulant and Skew Circulant Splitting Methods for Hermitian Positive Definite Toeplitz Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
N. Akhondi ◽  
F. Toutounian
Keyword(s):  
Convergence Property ◽  
Linear Equations ◽  
Coefficient Matrix ◽  
Positive Definite ◽  
Optimal Parameters ◽  
Skew Circulant ◽  
Systems Of Linear Equations ◽  
Toeplitz Systems ◽  
Two Parameters ◽  
Two Parameter

We study the CSCS method for large Hermitian positive definite Toeplitz linear systems, which first appears in Ng's paper published in (Ng, 2003), and CSCS stands for circulant and skew circulant splitting of the coefficient matrix . In this paper, we present a new iteration method for the numerical solution of Hermitian positive definite Toeplitz systems of linear equations. The method is a two-parameter generation of the CSCS method such that when the two parameters involved are equal, it coincides with the CSCS method. We discuss the convergence property and optimal parameters of this method. Finally, we extend our method to BTTB matrices. Numerical experiments are presented to show the effectiveness of our new method.

scholarly journals Supercomputing in the South Pacific: performance of a parallel cluster using existing USP facilities

2004 ◽  
Vol 22 (1) ◽  
pp. 67
Author(s):  
William J Blanke ◽  
Imtiyaz Hussein
Keyword(s):  
High Performance ◽  
Linear Equations ◽  
Leading Edge ◽  
South Pacific ◽  
The South ◽  
Systems Of Linear Equations ◽  
Linpack Benchmark ◽  
Large Systems ◽  
Low Efficiency ◽  
The University

This paper presents the details of a parallel computing cluster built using existing computing resources at the University of the South Pacific. Benchmarking tests using the High Performance Linpack Benchmark were done in order to measure the gigaflops (billions of floating point operations per second) ratings for solving large systems of linear equations while varying the number of computers and Ethernet switches used. These tests provided an overall maximum gigaflops rating which allowed comparison of USP's cluster with leading edge clusters from around the world. Efficiency results also provided insight in how improving the existing network infrastructure might improve the performance of USP's cluster and increase its gigaflops rating. Further tests revealed that the number of Ethernet switches used in USP's current network layout is a definite contributor to the low efficiency of the system as a whole.

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