A communication-less parallel algorithm for tridiagonal Toeplitz systems
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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.
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About: This article is published in Journal of Computational and Applied Mathematics. The article was published on 20 Feb 2008. and is currently open access. The article focuses on the topics: Toeplitz matrix & Tridiagonal matrix.
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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].
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A fast algorithm for solving tridiagonal quasi-Toeplitz linear systems
TL;DR: An efficient algorithm for solving the tridiagonal quasi-Toeplitz linear systems is proposed, which takes more floating-point operations (FLOPS) than the L U decomposition method, but needs less memory storage and data transmission and is about twice faster than theL U decompose method.
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A highly scalable parallel algorithm for solving Toeplitz tridiagonal systems of linear equations
TL;DR: A modification of the "Dichotomy Algorithm" (Terekhov, 2010) is proposed, aimed at parallel realization of a broad class of numerical methods including the inversion of Toeplitz and quasi-Toeplitzer tridiagonal matrices.
A conservative overlap method for multi-block parallelization of compact finite-volume schemes
TL;DR: A reasonable trade-off between accuracy and performances is discussed in the paper with reference to both the spectral properties of the method and the results of fully turbulent numerical simulations.
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Vectorized Parallel Solver for Tridiagonal Toeplitz Systems of Linear Equations.
Beata Dmitruk,Przemyslaw Stpiczynski +1 more
- 08 Sep 2019
TL;DR: Two versions of a new divide and conquer parallel algorithm for solving tridiagonal Toeplitz systems of linear equations based on a recently developed algorithm for solve linear recurrence systems are presented.
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References
Application and accuracy of the parallel diagonal dominant algorithm
Xian-He Sun
- 01 Aug 1995
TL;DR: A detailed study of the PDD algorithm is given, which is extended to solve periodic tridiagonal systems and its scalability is studied, and the reduced PDD algorithms are proposed, which has a smaller operation count than that of the conventional sequential algorithm for many applications.
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.
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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.
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A split-correct parallel algorithm for solving tridiagonal symmetric toeplitz systems
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.
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