A fully parallel method for the singular eigenvalue problem

Li, Kuiyuan; Uvah, Josaphat; Zhao, Shengzhi

doi:10.1016/j.camwa.2004.03.017

Cited by 1 publication

(2 citation statements)

References 9 publications

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“…Therefore, assuming 2t < n the first n 2 equations do not require correcting and are acceptable as approximate solutions to the true solution without being corrected. For system (3) we see that only the first t equations of x are not within the given acceptable tolerance levels (easily shown from a UL implementation of the algorithm in Yan and Chung [10]) implying that the last n 2 solutions are within the given tolerance and do not require correction. Combining these results, we present the following theorem:…”

Section: The Stacked Method-2 Processorsmentioning

confidence: 92%

“…It has been well established in McNally [4], McNally et al [6] and Nemani [7] that this is a well motivated and frequently occurring problem which arises in such application areas as second order differential equations, signal/image processing and numerical solutions to integral equations [3,9]. In Rojo [8] an algorithm was presented for exactly solving system (1) when = 1 based upon the perturbation A = LU + P and in Yan and Chung [10] a fast algorithm was presented for approximating the solution to within a given tolerance.…”

Section: Introductionmentioning

confidence: 99%

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A communication-less parallel algorithm for tridiagonal Toeplitz systems

McNally

Garey

Shaw

2008

Journal of Computational and Applied Mathematics

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Diagonally dominant tridiagonal Toeplitz systems of linear equations arise in many application areas and have been well studied in the past. Modern interest in numerical linear algebra is often focusing on solving classic problems in parallel. In McNally [Fast parallel algorithms for tri-diagonal symmetric Toeplitz systems, MCS Thesis, University of New Brunswick, Saint John, 1999], an m processor Split & Correct algorithm was presented for approximating the solution to a symmetric tridiagonal Toeplitz linear system of equations. Nemani [Perturbation methods for circulant-banded systems and their parallel implementation, Ph.D. Thesis, University of New Brunswick, Saint John, 2001] and McNally (2003) adapted the works of Rojo [A new method for solving symmetric circulant tri-diagonal system of linear equations, Comput. Math. Appl. 20 (1990) 61-67], Yan and Chung [A fast algorithm for solving special tri-diagonal systems, Computing 52 (1994) 203-211] and McNally et al. [A split-correct parallel algorithm for solving tri-diagonal symmetric Toeplitz systems, Internat. J. Comput. Math. 75 (2000) 303-313] to the non-symmetric case. In this paper we present relevant background from these methods and then introduce an m processor scalable communication-less approximation algorithm for solving a diagonally dominant tridiagonal Toeplitz system of linear equations.

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Section: The Stacked Method-2 Processorsmentioning

confidence: 92%