Representations and expansions of weighted pseudoinverse matrices, iterative methods, and problem regularization. I. Positive definite weights

Authors:
I. V. Sergienko;E. F. Galba;V. S. Deineka
Affiliations:
V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine;V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine;V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine
Venue:
Cybernetics and Systems Analysis
Year:
2008

Citing 15
Cited 1

Matrix analysis

Matrix analysis
A recursive algorithm for computing the weighted Moore-Penrose inverse A+-MN-

Journal of Computational Mathematics
A finite algorithm for computing the weighted Moore-Penrose inverse +-mn-

Applied Mathematics and Computation
Algebraic properties of classes of concommuting and H-selfadjoint matrices

Computational Mathematics and Mathematical Physics
Iterative methods for calculating a weighted pseudoinverse

Computational Mathematics and Mathematical Physics
Introduction to matrix analysis (2nd ed.)

Introduction to matrix analysis (2nd ed.)
Component averaging: An efficient iterative parallel algorithm for large and sparse unstructured problems

Parallel Computing
The representation and approximation for the weighted Moore—Penrose inverse

Applied Mathematics and Computation
Block-Iterative Algorithms with Diagonally Scaled Oblique Projections for the Linear Feasibility Problem

SIAM Journal on Matrix Analysis and Applications
On the Method of Weighting for Equality Constrained Least Squares Problems

On the Method of Weighting for Equality Constrained Least Squares Problems
Limiting Representations of Weighted Pseudoinverse Matrices with Positive Definite Weights. Problem Regularization

Cybernetics and Systems Analysis
Iterative methods with different rates of convergence for calculating weighted pseudoinverse matrices and weighted normal pseudosolutions with positive definite weights

Cybernetics and Systems Analysis
Handbook for Automatic Computation: Linear Algebra (Grundlehren Der Mathematischen Wissenschaften, Vol 186)

Handbook for Automatic Computation: Linear Algebra (Grundlehren Der Mathematischen Wissenschaften, Vol 186)
Series expansion of weighted pseudoinverse matrices and iterative methods for calculating weighted pseudoinverse matrices and weighted normal pseudosolutions

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

Cybernetics and Systems Analysis

Representations and expansions of weighted pseudoinverse matrices, iterative methods, and problem regularization. II. Singular weights

Cybernetics and Systems Analysis

Quantified Score

Hi-index	0.00

Visualization

Abstract

The paper reviews studies on the representations and expansions of weighted pseudoinverse matrices with positive definite weights and on iterative methods and regularized problems for calculation of weighted pseudoinverse matrices and weighted normal pseudosolutions. The use of these methods to solve constrained least-squares problems is examined.