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Acceleration of one-parameter relaxation methods for singular saddle point problems

Jae Heon Yun
대한수학회 (The Korean Mathematical Society)|2016.05|대한수학회지 (Journal of the KMS)|제53권 제3호|pp. 691-707

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키워드

singular saddle point problemsemi-convergencerelaxation iterative methodpseudo-spectral radiusscaled preconditioner
주제분류수학

초록

In this paper, we first introduce two one-parameter relaxation (OPR) iterative methods for solving singular saddle point problems whose semi-convergence rate can be accelerated by using scaled preconditioners. Next we present formulas for finding their optimal parameters which yield the best semi-convergence rate. Lastly, numerical experiments are provided to examine the efficiency of the OPR methods with scaled preconditioners by comparing their performance with the parameterized Uzawa method with optimal parameters.

Abstract

In this paper, we first introduce two one-parameter relaxation (OPR) iterative methods for solving singular saddle point problems whose semi-convergence rate can be accelerated by using scaled preconditioners. Next we present formulas for finding their optimal parameters which yield the best semi-convergence rate. Lastly, numerical experiments are provided to examine the efficiency of the OPR methods with scaled preconditioners by comparing their performance with the parameterized Uzawa method with optimal parameters.

참고문헌 (24)

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관련 논문AI추천

SEMI-CONVERGENCE OF THE PARAMETERIZED INEXACT UZAWA METHOD FOR SINGULAR SADDLE POINT PROBLEMS윤재헌대한수학회 · 대한수학회보2015 · 제52권 제5호CONVERGENCE OF RELAXED TWO-STAGE MULTISPLITTING METHOD USING AN OUTER SPLITTING윤재헌대한수학회 · 대한수학회보2010 · 제47권 제4호COMPARISON RESULTS FOR THE PRECONDITIONED GAUSS-SEIDEL METHODS윤재헌대한수학회 · 대한수학회논문집2012 · 제27권 제1호Preconditioners for a coupled problem by a penalty term arisen in an augmented Lagrangian method박은희, 이창옥대한수학회 · 대한수학회지2020 · 제57권 제5호Parallel performance of multisplitting methods with preweighting윤재헌, 한유두대한수학회 · 대한수학회지2012 · 제49권 제4호Preconditioned SSOR methods for the linear complementarity problem with $M$-matrixDan Zhang대한수학회 · 대한수학회논문집2019 · 제34권 제2호

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