Ill-conditioning of the truncated singular value decomposition, Tikhonov regularization and their applications to numerical partial differential equations.
type: Item
instance of: scholarly article
zbMATH Open document ID: 1249.65087
author: Zi-Cai Li
author: Hung-Tsai Huang
author: Yimin Wei
published in: Numerical Linear Algebra with Applications
publication date: 2012-06-07T00:00:00Z
Mathematics Subject Classification ID: 65F22
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 65N20
Mathematics Subject Classification ID: 65F20
Mathematics Subject Classification ID: 65F35
Mathematics Subject Classification ID: 65N35
zbMATH DE Number: 6043433
zbMATH Keywords: ill-conditioning
zbMATH Keywords: truncated singular value decomposition
zbMATH Keywords: Tikhonov regularization
zbMATH Keywords: effective condition number
zbMATH Keywords: collocation Trefftz method
describes a project that uses: Regularization tools
describes a project that uses: mctoolbox
MaRDI profile type: Publication
full work available at URL: nla.766
OpenAlex ID: W2066549325
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DOI: 10.1002/NLA.766
title: Ill-conditioning of the truncated singular value decomposition, Tikhonov regularization and their applications to numerical partial differential equations.
review text: This paper explores some intrinsic characteristics of accuracy and stability for the truncated singular value decomposition (TSVD) and the Tikhonov regularization (TR). Both regularization techniques are applied to numerical solutions of partial differential equations (PDE).NEWLINENEWLINEThe authors derive new bounds for the contition number and the effective condition number, which is used to improve conditioning by TSVD and TR. A brief error analysis is done and error bounds are derived. The obtained results are illustrated by numerical experiments with the discrete Laplace equation.
reviewed by: Martin Plešinger
description: scientific article; zbMATH DE number 6043433