Expansion of weighted pseudoinverse matrices with positive definite weights into matrix power products. Iterative methods

被引：0

作者：

Sergienko I.V. ^{[1
]}

Galba E.F. ^{[1
]}

Deineka V.S. ^{[1
]}

机构：

[1] V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv

来源：

Cybernetics and Systems Analysis | 2007年 / 43卷 / 1期

关键词：

Constrained least-squares problems; Iterative methods; Matrix power products; Weighted normal pseudosolutions; Weighted pseudoinverse matrices;

D O I：

10.1007/s10559-007-0024-z

中图分类号：

学科分类号：

摘要：

Weighted pseudoinverse matrices with positive definite weights are expanded into matrix power products with negative exponents and arbitrary positive parameters. These expansions are used to develop and analyze iterative methods for evaluating weighted pseudoinverse matrices and weighted normal pseudosolutions and solving constrained least-squares problems. © Springer Science+Business Media, Inc. 2007.

引用

页码：34 / 49

页数：15

共 26 条

[1] Expansion of weighted pseudoinverse matrices with singular weights into matrix power products and iteration methods
Sergienko I.V.
Galba E.F.
Deineka V.S.
Ukrainian Mathematical Journal, 2007, 59 (9) : 1417 - 1440
[2] Expansion of weighted pseudoinverse matrices in matrix power products
Sergienko I.V.
Galba E.F.
Deineka V.S.
Ukrainian Mathematical Journal, 2004, 56 (11) : 1828 - 1848
[3] Iterative methods with different rates of convergence for calculating weighted pseudoinverse matrices and weighted normal pseudosolutions with positive definite weights
I. V. Sergienko
E. F. Galba
V. S. Deineka
Cybernetics and Systems Analysis, 2004, 40 (5) : 643 - 664
[4] Representations and expansions of weighted pseudoinverse matrices, iterative methods, and problem regularization. I. Positive definite weights
Sergienko I.V.
Galba E.F.
Deineka V.S.
Cybernetics and Systems Analysis, 2008, 44 (1) : 36 - 55
[5] Series expansion of weighted pseudoinverse matrices and iterative methods for calculating weighted pseudoinverse matrices and weighted normal pseudosolutions
Sergienko I.V.
Galba E.F.
Deineka V.S.
Cybernetics and Systems Analysis, 2006, 42 (01) : 28 - 53
[6] Limiting Representations of Weighted Pseudoinverse Matrices with Positive Definite Weights. Problem Regularization
I. V. Sergienko
E. F. V. S. Galba
Cybernetics and Systems Analysis, 2003, 39 (6) : 816 - 830
[7] Methods of computing weighted pseudoinverse matrices with singular weights
E. F. Galba
I. N. Molchanov
V. V. Skopetskii
Cybernetics and Systems Analysis, 1999, 35 : 814 - 831
[8] Iterative methods to compute weighted normal pseudosolutions with positive definite weights
Galba, EF
CYBERNETICS AND SYSTEMS ANALYSIS, 1998, 34 (02) : 245 - 253
[9] Iterative methods to compute weighted normal pseudosolutions with positive definite weights
E. F. Galba
Cybernetics and Systems Analysis, 1998, 34 : 245 - 253
[10] Methods of computing weighted pseudoinverse matrices with singular weights
Galba, EF
Molchanov, IN
Skopetskii, VV
CYBERNETICS AND SYSTEMS ANALYSIS, 1999, 35 (05) : 814 - 831

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