Fast iterative methods for sinc systems

Michael K. Ng; Daniel Potts

doi:10.1137/S0895479800369773

Fast iterative methods for sinc systems

Michael K. Ng^*, Daniel Potts

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

11 Citations (Scopus)

Abstract

We consider linear systems of equations arising from the sinc method of boundary value problems which are typically nonsymmetric and dense. For the solutions of these systems we propose Krylov subspace methods with banded preconditioners. We prove that our preconditioners are invertible and discuss the convergence behavior of the conjugate gradient method for normal equations (CGNE). In particular, we show that the solution of an n-by-n discrete sinc system arising from the model problem can be obtained in O(n log² n) operations by using the preconditioned CGNE method. Numerical results are given to illustrate the effectiveness of our fast iterative solvers.

Original language	English
Pages (from-to)	581-598
Number of pages	18
Journal	SIAM Journal on Matrix Analysis and Applications
Volume	24
Issue number	2
DOIs	https://doi.org/10.1137/S0895479800369773
Publication status	Published - Jan 2002

Scopus Subject Areas

Analysis

User-Defined Keywords

Banded matrices
Krylov subspace methods
Preconditioners
Sinc method
Toeplitz matrices

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10.1137/S0895479800369773

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title = "Fast iterative methods for sinc systems",

abstract = "We consider linear systems of equations arising from the sinc method of boundary value problems which are typically nonsymmetric and dense. For the solutions of these systems we propose Krylov subspace methods with banded preconditioners. We prove that our preconditioners are invertible and discuss the convergence behavior of the conjugate gradient method for normal equations (CGNE). In particular, we show that the solution of an n-by-n discrete sinc system arising from the model problem can be obtained in O(n log2 n) operations by using the preconditioned CGNE method. Numerical results are given to illustrate the effectiveness of our fast iterative solvers.",

keywords = "Banded matrices, Krylov subspace methods, Preconditioners, Sinc method, Toeplitz matrices",

author = "Ng, {Michael K.} and Daniel Potts",

note = "The work described in this paper wassupported by a grant from the German Academic Exchange Services and the Research Grants Councilof the Hong Kong Joint Research Scheme (project G-HK020/00). The research of this author was supported in part by RGC grant 7132/00P and HKU CRCG grants 10203501, 10203907, and 10203408. The research of this author was supported in part by the Hong Kong–German Joint Research Collaboration Grant from the Deutscher Akademischer Austauschdienst and the Hong Kong Research Grants Council. Copyright {\textcopyright} 2002 Society for Industrial and Applied Mathematics",

year = "2002",

month = jan,

doi = "10.1137/S0895479800369773",

language = "English",

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T1 - Fast iterative methods for sinc systems

AU - Ng, Michael K.

AU - Potts, Daniel

N1 - The work described in this paper wassupported by a grant from the German Academic Exchange Services and the Research Grants Councilof the Hong Kong Joint Research Scheme (project G-HK020/00). The research of this author was supported in part by RGC grant 7132/00P and HKU CRCG grants 10203501, 10203907, and 10203408. The research of this author was supported in part by the Hong Kong–German Joint Research Collaboration Grant from the Deutscher Akademischer Austauschdienst and the Hong Kong Research Grants Council. Copyright © 2002 Society for Industrial and Applied Mathematics

PY - 2002/1

Y1 - 2002/1

N2 - We consider linear systems of equations arising from the sinc method of boundary value problems which are typically nonsymmetric and dense. For the solutions of these systems we propose Krylov subspace methods with banded preconditioners. We prove that our preconditioners are invertible and discuss the convergence behavior of the conjugate gradient method for normal equations (CGNE). In particular, we show that the solution of an n-by-n discrete sinc system arising from the model problem can be obtained in O(n log2 n) operations by using the preconditioned CGNE method. Numerical results are given to illustrate the effectiveness of our fast iterative solvers.

AB - We consider linear systems of equations arising from the sinc method of boundary value problems which are typically nonsymmetric and dense. For the solutions of these systems we propose Krylov subspace methods with banded preconditioners. We prove that our preconditioners are invertible and discuss the convergence behavior of the conjugate gradient method for normal equations (CGNE). In particular, we show that the solution of an n-by-n discrete sinc system arising from the model problem can be obtained in O(n log2 n) operations by using the preconditioned CGNE method. Numerical results are given to illustrate the effectiveness of our fast iterative solvers.

KW - Banded matrices

KW - Krylov subspace methods

KW - Preconditioners

KW - Sinc method

KW - Toeplitz matrices

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U2 - 10.1137/S0895479800369773

DO - 10.1137/S0895479800369773

M3 - Journal article

AN - SCOPUS:0037265672

SN - 0895-4798

VL - 24

SP - 581

EP - 598

JO - SIAM Journal on Matrix Analysis and Applications

JF - SIAM Journal on Matrix Analysis and Applications

IS - 2

ER -

Fast iterative methods for sinc systems

Abstract

Scopus Subject Areas

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