Weighted Tikhonov filter matrices for ill-posed problems

Yimin Wei; Michael Ng

doi:10.1016/S0096-3003(03)00149-8

Weighted Tikhonov filter matrices for ill-posed problems

Yimin Wei, Michael Ng^*

^*Corresponding author for this work

Department of Mathematics

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

6 Citations (Scopus)

Abstract

We consider the concept of weighted Tikhonov filter matrices in connection to discrete ill-posed and rank-deficient linear problems. Some properties of the weighted Tikhonov filter matrices are given together with their filtering and regularization effects. We also present perturbation identities for the weighted Tikhonov regularized linear least squares problem using weighted filter matrices generalizing well known weighted perturbation identities for the weighted linear least squares problem and weighted pseudoinverses.

Original language	English
Pages (from-to)	411-422
Number of pages	12
Journal	Applied Mathematics and Computation
Volume	149
Issue number	2
DOIs	https://doi.org/10.1016/S0096-3003(03)00149-8
Publication status	Published - 12 Feb 2004

Scopus Subject Areas

Computational Mathematics
Applied Mathematics

User-Defined Keywords

Filter matrices
Rank deficient
Weighted pseudoinverse
Weighted Tikhonov regularization

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10.1016/S0096-3003(03)00149-8

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title = "Weighted Tikhonov filter matrices for ill-posed problems",

abstract = "We consider the concept of weighted Tikhonov filter matrices in connection to discrete ill-posed and rank-deficient linear problems. Some properties of the weighted Tikhonov filter matrices are given together with their filtering and regularization effects. We also present perturbation identities for the weighted Tikhonov regularized linear least squares problem using weighted filter matrices generalizing well known weighted perturbation identities for the weighted linear least squares problem and weighted pseudoinverses.",

keywords = "Filter matrices, Rank deficient, Weighted pseudoinverse, Weighted Tikhonov regularization",

author = "Yimin Wei and Michael Ng",

note = "Research supported by Project 19901006, National Natural Science Foundation of China and Doctoral Point Foundation of China. Partial work was finished when the author visited Harvard University and supported by China Scholarship Council. Research supported in part by RGC Grant no. 7132/00P and HKU CRCG Grant nos. 10203501, 10203907 and 10203408. Publisher Copyright: {\textcopyright} 2003 Elsevier Inc. All rights reserved.",

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T1 - Weighted Tikhonov filter matrices for ill-posed problems

AU - Wei, Yimin

AU - Ng, Michael

N1 - Research supported by Project 19901006, National Natural Science Foundation of China and Doctoral Point Foundation of China. Partial work was finished when the author visited Harvard University and supported by China Scholarship Council. Research supported in part by RGC Grant no. 7132/00P and HKU CRCG Grant nos. 10203501, 10203907 and 10203408. Publisher Copyright: © 2003 Elsevier Inc. All rights reserved.

PY - 2004/2/12

Y1 - 2004/2/12

N2 - We consider the concept of weighted Tikhonov filter matrices in connection to discrete ill-posed and rank-deficient linear problems. Some properties of the weighted Tikhonov filter matrices are given together with their filtering and regularization effects. We also present perturbation identities for the weighted Tikhonov regularized linear least squares problem using weighted filter matrices generalizing well known weighted perturbation identities for the weighted linear least squares problem and weighted pseudoinverses.

AB - We consider the concept of weighted Tikhonov filter matrices in connection to discrete ill-posed and rank-deficient linear problems. Some properties of the weighted Tikhonov filter matrices are given together with their filtering and regularization effects. We also present perturbation identities for the weighted Tikhonov regularized linear least squares problem using weighted filter matrices generalizing well known weighted perturbation identities for the weighted linear least squares problem and weighted pseudoinverses.

KW - Filter matrices

KW - Rank deficient

KW - Weighted pseudoinverse

KW - Weighted Tikhonov regularization

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U2 - 10.1016/S0096-3003(03)00149-8

DO - 10.1016/S0096-3003(03)00149-8

M3 - Journal article

AN - SCOPUS:0348170680

SN - 0096-3003

VL - 149

SP - 411

EP - 422

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

IS - 2

ER -

Weighted Tikhonov filter matrices for ill-posed problems

Abstract

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