Stable solutions of linear systems involving long chain of matrix multiplications |
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Authors: | Zhaojun Bai Cherung Lee |
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Institution: | a Department of Computer Science, University of California, Davis, CA 95616, USA b Department of Computer Science, National Tsing Hua University, Hsinchu, Taiwan c Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019, USA d School of Mathematical Sciences, Peking University, Beijing 100871, PR China |
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Abstract: | This paper is concerned with solving linear system (In+BL?B2B1)x=b arising from the Green’s function calculation in the quantum Monte Carlo simulation of interacting electrons. The order of the system and integer L are adjustable. Also adjustable is the conditioning of the coefficient matrix to give rise an extreme ill-conditioned system. Two numerical methods based on the QR decomposition with column pivoting and the singular value decomposition, respectively, are studied in this paper. It is proved that the computed solution by each of the methods is weakly backward stable in the sense that the computed is close to the exact solution of a nearby linear system |
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Keywords: | 15A09 15A12 65F05 65F35 82B80 |
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