Expansion of weighted pseudoinverse matrices with singular weights into matrix power products and iteration methods

被引：0

作者：

Sergienko I.V. ^{[1
]}

Galba E.F. ^{[1
]}

Deineka V.S. ^{[1
]}

机构：

[1] Institute of Cybernetics, Ukrainian National Academy of Sciences, Kiev

来源：

Ukrainian Mathematical Journal | 2007年 / 59卷 / 9期

关键词：

Iteration Process; Singular Weight; Weighted Normal Pseudosolution; Weighted Pseudoinverse Matrice; Matrix Power Series;

D O I：

10.1007/s11253-007-0096-y

中图分类号：

学科分类号：

摘要：

We obtain expansions of weighted pseudoinverse matrices with singular weights into matrix power products with negative exponents and arbitrary positive parameters. We show that the rate of convergence of these expansions depends on a parameter. On the basis of the proposed expansions, we construct and investigate iteration methods with quadratic rate of convergence for the calculation of weighted pseudoinverse matrices and weighted normal pseudosolutions. Iteration methods for the calculation of weighted normal pseudosolutions are adapted to the solution of least-squares problems with constraints. © 2007 Springer Science+Business Media, Inc.

引用

页码：1417 / 1440

页数：23