NDLI: On Preconditioned Iterative Methods for Certain Time-Dependent Partial Differential Equations

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Bai, Zhong-Zhi Huang, Yu-Mei Ng, Michael K.
Copyright Year	2009
Abstract	When the Newton method or the fixed-point method is employed to solve the systems of nonlinear equations arising in the sinc-Galerkin discretization of certain time-dependent partial differential equations, in each iteration step we need to solve a structured subsystem of linear equations iteratively by, for example, a Krylov subspace method such as the preconditioned GMRES. In this paper, based on the tensor and the Toeplitz structures of the linear subsystems we construct structured preconditioners for their coefficient matrices and estimate the eigenvalue bounds of the preconditioned matrices under certain assumptions. Numerical examples are given to illustrate the effectiveness of the proposed preconditioning methods. It has been shown that a combination of the Newton/fixed-point iteration with the preconditioned GMRES method is efficient and robust for solving the systems of nonlinear equations arising from the sinc-Galerkin discretization of the time-dependent partial differential equations.
Starting Page	1019
Ending Page	1037
Page Count	19
File Format	PDF
ISSN	00361429
DOI	10.1137/080718176
e-ISSN	10957170
Issue Number	2
Volume Number	47
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2009-02-13
Access Restriction	Subscribed
Subject Keyword	GMRES method time-dependent partial differential equation Iterative methods for linear systems Eigenvalues, eigenvectors sinc-Galerkin discretization Toeplitz-like matrix eigenvalue bound preconditioning
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Numerical Analysis Computational Mathematics

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