Journal Article10.1016/J.AMC.2006.06.058
A parallel iterative method for solving periodical block-tridiagonal linear equations
Xiao Manyu,Lu Quanyi +1 more
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TL;DR: Based upon splitting the coefficient matrix, a parallel iterative algorithm for periodical block-tridiagonal linear equations on distributed-memory multi-computers is proposed, which is more general applied than that presented in Lihua Chi, Jie Liu, Xiaomei Li.
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About: This article is published in Applied Mathematics and Computation. The article was published on 15 Jan 2007. The article focuses on the topics: Tridiagonal matrix algorithm & Tridiagonal matrix.
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Citations
A fast parallel algorithm for solving block-tridiagonal systems of linear equations including the domain decomposition method
TL;DR: This study develops a new parallel algorithm for solving systems of linear algebraic equations with the same block-tridiagonal matrix but with different right-hand sides and proposes a parallel realization of the domain decomposition method (the Schur complement method).
A Parallel Direct Algorithm Based on Matrix Decomposition for Solving Periodical Block-Tridiagonal Linear Equations
樊艳红,吕全义,李纪华,宋东红 +3 more
TL;DR: A parallel direct algorithm for solving periodical block-tridiagonal linear equations is presented, utilizing matrix decomposition and minimizing communication between processors, with theoretical and numerical results demonstrating its effectiveness and preferable parallelism.
A Parallel Algorithm of Block Tridiagonal Systems for the Initial Boundary Value Problem of 2D-Hyperbolic Equation
ZHANG Heng,ZHANG Wu +1 more
TL;DR: A parallel algorithm for solving 2D-hyperbolic equations is proposed, achieving line speedup and over 90% parallel efficiency on the ZiQiang 3000 supercomputer, with numerical results matching theoretical analysis for the initial boundary value problem.
References
A parallel algorithm for solving Toeplitz linear systems
L. E. Garey,R. E. Shaw +1 more
TL;DR: This paper combines the two approaches which will allow application of the cyclic reduction method to coefficient matrices of more general forms, and the convergence of the approximations to the exact solution is examined.
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A direct method for solving circulant tridiagonal block systems of linear equations
TL;DR: A modification of Rojo's algorithm to solve block circulant tridiagonal systems of linear equations which are Toeplitz and Hermitian is presented, based on obtaining the solution of the nonlinear matrix equation [email protected]+B*@C^-^1B.
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•Journal Article
An effective parallel algorithm for tridiagonal linear equations
TL;DR: A parallel algorithm,PPD algorithm, for the solution of diagonally dominant tridiagonal linear systems, and the results show that speedup improves linearly and the efficiency of the method is up to 90%.
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