Journal Article10.1080/00207160008804986
A split-correct parallel algorithm for solving tridiagonal symmetric toeplitz systems
17
TL;DR: A method will be presented which will allow for problems of the above nature to be split into two separate systems which can be solved in parallel, and then combined and corrected to obtain a solution to the original system.
read more
Abstract: In 1994, Yan and Chung produced a fast algorithm for solving a diagonally dominant symmetric Toeplitz tridiagonal system of linear equations Ax = b. In this work a method will be presented which will allow for problems of the above nature to be split into two separate systems which can be solved in parallel, and then combined and corrected to obtain a solution to the original system. An error analysis will be provided along with example cases and time comparison results.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
A fast algorithm for solving diagonally dominant symmetric pentadiagonal Toeplitz systems
TL;DR: This paper derives a new algorithm for solving symmetric pentadiagonal Toeplitz systems of linear equations based upon a technique used in [J.M. McNally, L.E. Shaw, A split-correct parallel algorithm for solve tri-diagonal symmetric ToePlitz systems, Int. Comput. Math. 75 (2000) 303-313].
21
A parallel method for linear equations with tridiagonal Toeplitz coefficient matrices
L.E. Garey,R. E. Shaw +1 more
TL;DR: Nonsymmetric Toepliz systems and nonsymmetric circulant systems are examined and the coefficient matrix is split into two bidiagonal matrices and the efficient solution of the resulting systems is considered.
19
A communication-less parallel algorithm for tridiagonal Toeplitz systems
TL;DR: In this article, the authors presented an m processor scalable communication-less approximation algorithm for solving a diagonally dominant tridiagonal Toeplitz system of linear equations and adapted the works of Rojo and McNally et al. to the non-symmetric case.
13
Fast solvers for tridiagonal Toeplitz linear systems
TL;DR: This paper first considers the case of A being subdiagonally dominant, then transforms A into a block matrix by an elementary transformation and solves such a linear system using the block LU factorization.
References
•Book
Introduction to Parallel Algorithms and Architectures: Arrays, Trees, Hypercubes
F. Thomson Leighton
- 01 Sep 1991
TL;DR: This chapter discusses sorting on a Linear Array with a Systolic and Semisystolic Model of Computation, which automates the very labor-intensive and therefore time-heavy and expensive process of manually sorting arrays.
3.1K
•Book
Applied numerical analysis
Curtis F. Gerald,Patrick O. Wheatley +1 more
- 01 Jan 1970
TL;DR: The fifth edition of this book as mentioned in this paper continues teaching numerical analysis and techniques, and is suitable for students with mathematics and engineering backgrounds, the breadth of topics (partial differential equations, systems of nonlinear equations, and matrix algebra), provide comprehensive and flexible coverage of numerical analysis.
2.3K
A new method for solving symmetric circulant tridiagonal systems of linear equations
TL;DR: A new method for computing the solution of a linear system having a symmetric circulant tridiagonal matrix is presented, which is quite competitive with Gaussian elimination and with the modified double sweep method.
45
A fast algorithm for solving special tridiagonal systems
Wen-Ming Yan,Kuo-Liang Chung +1 more
TL;DR: A fast algorithm for solving the special tridiagonal system, a symmetric diagonally dominant and Toeplitz system of linear equations, which is quite competitive with the Gaussian elimination, cyclic reduction, specialLU factorization, reversed triangular factorizations, and ToEplitz factorization methods.
40