Journal Article10.1016/0167-8191(90)90131-R
A parallel algorithm solving a tridiagonal Toeplitz linear system
Hyoung Joong Kim,Jang Gyu Lee +1 more
- 01 Mar 1990
- Vol. 13, Iss: 3, pp 289-294
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TL;DR: The solver based on the modified Gaussian elimination method fully exploits parallelism and Computation and communication complexities of the proposed algorithm are all shown to be O(n/m).
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Abstract: A new tridiagonal Toeplitz linear system (TTLS) solver is proposed. The solver first decomposes an n-dimensional strictly diagonally dominant TTLS equation into a number of m-dimensional subsystems employing a modified Gaussian elimination method. An analytic solution of a continued fraction is obtained to derive the solver. The solver based on the modified Gaussian elimination method fully exploits parallelism. Computation and communication complexities of the proposed algorithm are all shown to be O(n/m).
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Citations
Patent
Data processing method and apparatus employing parallel processing for solving systems of linear equations
Mochizuki Yoshiyuki
- 13 Jul 1992
TL;DR: A linear calculating equipment as discussed by the authors comprises a memory for storing a coefficient matrix, a known vector and an unknown vector of a given system of linear equations, a pivoting device for choosing pivots of the matrix and a plurality of preprocessors for executing K steps of preprocessing for multi-pivot simultaneous elimination.
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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.
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.
•Dissertation
Design and evaluation of tridiagonal solvers for vector and parallel computers
Larriba Pey,Josep Lluís +1 more
- 10 Mar 1995
TL;DR: In this paper, the authors discuss the resolution of SISTEMAS TRIDIAGONALES DE ECUACIONES in the context of a new metoda.
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References
A Fast Direct Solution of Poisson's Equation Using Fourier Analysis
TL;DR: This work has developed a direct method of solution involving Fourier analysis which can solve Poisson''s equation in a square region covered by a 48 x 48 mesh in 0.9 seconds on the IBM 7090.
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