Preconditioned Iterative Methods for Weighted Toeplitz Least Squares Problems

Michele Benzi; Michael K. Ng

doi:10.1137/040616048

Preconditioned Iterative Methods for Weighted Toeplitz Least Squares Problems

Michele Benzi^*
, Michael K. Ng

^*Corresponding author for this work

Department of Mathematics

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

72 Citations (Scopus)

199 Downloads (Pure)

Abstract

We consider the iterative solution of weighted Toeplitz least squares problems. Our approach is based on an augmented system formulation. We focus our attention on two types of preconditioners: a variant of constraint preconditioning, and the Hermitian/skew-Hermitian splitting (HSS) preconditioner. Bounds on the eigenvalues of the preconditioned matrices are given in terms of problem and algorithmic parameters, and numerical experiments are used to illustrate the performance of the preconditioners.

Original language	English
Pages (from-to)	1106-1124
Number of pages	19
Journal	SIAM Journal on Matrix Analysis and Applications
Volume	27
Issue number	4
DOIs	https://doi.org/10.1137/040616048
Publication status	Published - 31 Jul 2006

User-Defined Keywords

Augmented matrix
Constraint preconditioning
Eigenvalue bounds
Image restoration
Iterative methods
Preconditioning
Splittings

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10.1137/040616048

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title = "Preconditioned Iterative Methods for Weighted Toeplitz Least Squares Problems",

abstract = "We consider the iterative solution of weighted Toeplitz least squares problems. Our approach is based on an augmented system formulation. We focus our attention on two types of preconditioners: a variant of constraint preconditioning, and the Hermitian/skew-Hermitian splitting (HSS) preconditioner. Bounds on the eigenvalues of the preconditioned matrices are given in terms of problem and algorithmic parameters, and numerical experiments are used to illustrate the performance of the preconditioners.",

keywords = "Augmented matrix, Constraint preconditioning, Eigenvalue bounds, Image restoration, Iterative methods, Preconditioning, Splittings",

author = "Michele Benzi and Ng, \{Michael K.\}",

note = "Funding information: t Department of Mathematics and Computer Science, Emory University, Atlanta, GA 30322 ([email protected]). The work of this author was supported in part by National Science Foundation grant DMS-0207599. *Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong, and Department of Mathematics, Hong Kong Baptist University, Kowloow Tong, Hong Kong (mng@maths. hku.hk). The research of this author was supported in part by Hong Kong Research Grants Council grants HKU 7130/02P, HKU 7046/03P, and HKU 7035/04P, and HKU CRCG grants 10205964, 10205775, and 10204437. Publisher copyright: Copyright {\textcopyright} 2006 Society for Industrial and Applied Mathematics",

year = "2006",

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doi = "10.1137/040616048",

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T1 - Preconditioned Iterative Methods for Weighted Toeplitz Least Squares Problems

AU - Benzi, Michele

AU - Ng, Michael K.

N1 - Funding information: t Department of Mathematics and Computer Science, Emory University, Atlanta, GA 30322 ([email protected]). The work of this author was supported in part by National Science Foundation grant DMS-0207599. *Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong, and Department of Mathematics, Hong Kong Baptist University, Kowloow Tong, Hong Kong (mng@maths. hku.hk). The research of this author was supported in part by Hong Kong Research Grants Council grants HKU 7130/02P, HKU 7046/03P, and HKU 7035/04P, and HKU CRCG grants 10205964, 10205775, and 10204437. Publisher copyright: Copyright © 2006 Society for Industrial and Applied Mathematics

PY - 2006/7/31

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N2 - We consider the iterative solution of weighted Toeplitz least squares problems. Our approach is based on an augmented system formulation. We focus our attention on two types of preconditioners: a variant of constraint preconditioning, and the Hermitian/skew-Hermitian splitting (HSS) preconditioner. Bounds on the eigenvalues of the preconditioned matrices are given in terms of problem and algorithmic parameters, and numerical experiments are used to illustrate the performance of the preconditioners.

AB - We consider the iterative solution of weighted Toeplitz least squares problems. Our approach is based on an augmented system formulation. We focus our attention on two types of preconditioners: a variant of constraint preconditioning, and the Hermitian/skew-Hermitian splitting (HSS) preconditioner. Bounds on the eigenvalues of the preconditioned matrices are given in terms of problem and algorithmic parameters, and numerical experiments are used to illustrate the performance of the preconditioners.

KW - Augmented matrix

KW - Constraint preconditioning

KW - Eigenvalue bounds

KW - Image restoration

KW - Iterative methods

KW - Preconditioning

KW - Splittings

UR - https://www.scopus.com/pages/publications/33750169124

U2 - 10.1137/040616048

DO - 10.1137/040616048

M3 - Journal article

AN - SCOPUS:33750169124

SN - 0895-4798

VL - 27

SP - 1106

EP - 1124

JO - SIAM Journal on Matrix Analysis and Applications

JF - SIAM Journal on Matrix Analysis and Applications

IS - 4

ER -

Preconditioned Iterative Methods for Weighted Toeplitz Least Squares Problems

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