A diagonal preconditioner for singularly perturbed problems

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• 作者：Dana Černá ; Václav Finěk
• 关键词：wavelets ; singularly perturbed problems ; boundary value problems ; preconditioning
• 刊名：Boundary Value Problems
• 出版年：2017
• 出版时间：December 2017
• 年：2017
• 卷：2017
• 期：1
• 全文大小：1679KB
• 刊物主题：Difference and Functional Equations; Ordinary Differential Equations; Partial Differential Equations; Analysis; Approximations and Expansions; Mathematics, general;
• 出版者：Springer International Publishing
• ISSN：1687-2770
• 卷排序：2017

文摘

Using wavelet discretization with a standard wavelet diagonal preconditioning for singularly perturbed two-point boundary value problems, one can observe that condition numbers of arising stiffness matrices are growing with decreasing parameter ϵ when a nonsymmetric part starts to dominate. We propose here a simple diagonal preconditioning which significantly improves condition numbers of the stiffness matrices with a dominating nonsymmetric part and compare it with a standard wavelet preconditioning. Further, we prove that the condition numbers of diagonally preconditioned stiffness matrices are bounded independent of the matrix size. Numerical examples are given.