Some topics on weighted Moore-Penrose inverse, weighted least squares and weighted regularized Tikhonov problems
type: Item
instance of: scholarly article
title: Some topics on weighted Moore-Penrose inverse, weighted least squares and weighted regularized Tikhonov problems
zbMATH Open document ID: 1064.65032
author: Dingkun Wang
published in: Applied Mathematics and Computation
publication date: 2004-11-23T00:00:00Z
review text: \textit{D. J. Higham} [Linear Algebra Appl. 214, 193--213 (1995; Zbl 0816.15004)] gave the definition and formulae of the condition number under the spectral and Frobenius matrix norms in \(\mathbb{R}^{m\times n}\). The present author extends these results to two weighted matrix norms in \(\mathbb{C}^{m\times n}\). Moreover, the nearness to rank deficiency is considered. The regularized weighted Tikhonov problem is studied based on a generalized weighted singular value decomposition.
Mathematics Subject Classification ID: 65F22
Mathematics Subject Classification ID: 15A09
Mathematics Subject Classification ID: 65F20
Mathematics Subject Classification ID: 65F35
Mathematics Subject Classification ID: 15A12
zbMATH DE Number: 2117988
zbMATH Keywords: Condition number
zbMATH Keywords: Generalized weighted singular value decomposition
zbMATH Keywords: Nearness to rank deficiency
zbMATH Keywords: Structured condition number
zbMATH Keywords: Weighted Moore--Penrose inverse
zbMATH Keywords: Weighted linear least squares problem
reviewed by: A. Kukush
MaRDI profile type: Publication
full work available at URL: j.amc.2003.08.035
OpenAlex ID: W1995375949
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DOI: 10.1016/J.AMC.2003.08.035
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description: scientific article; zbMATH DE number 2117988