Journal Article10.1007/BF02238076
A fast algorithm for solving special tridiagonal systems
Wen-Ming Yan,Kuo-Liang Chung +1 more
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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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Abstract: In this paper, a fast algorithm for solving the special tridiagonal system is presented. This special tridiagonal system is a symmetric diagonally dominant and Toeplitz system of linear equations. The error analysis is also given. Our algorithm is quite competitive with the Gaussian elimination, cyclic reduction, specialLU factorization, reversed triangular factorization, and Toeplitz factorization methods. In addition, our result can be applied to solve the near-Toeplitz tridiagonal system. Some examples demonstrate the good efficiency and stability of our algorithm.
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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 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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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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