共查询到10条相似文献,搜索用时 74 毫秒
1.
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.
__________
Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 47–73, January–February 2008. 相似文献
2.
Weighted pseudoinverse matrices are expanded into matrix power series with negative exponents and arbitrary positive parameters.
Based on this expansion, iterative methods for evaluating weighted pseudoinverse matrices and weighted normal pseudosolutions
are designed and analyzed. The iterative methods for weighted normal pseudosolutions are extended to solving constrained least-squares
problems.
__________
Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 32–62, January–February 2006. 相似文献
3.
Three iterative processes are constructed and investigated for computing weighted pseudoinverse matrices with singular weights
and ML-weighted pseudoinverse matrices. Two of them are based on the decompositions of the weighted pseudoinverse matrix with
singular weights into matrix power series, and the third is a generalization of the Schulz method to nonsingular square matrices.
Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 150–169, September–October, 1999. 相似文献
4.
The paper reviews studies on the representations and expansions of weighted pseudoinverse matrices with positive semidefinite
weights and on the construction of iterative methods and regularized problems for the calculation of weighted pseudoinverses
and weighted normal pseudosolutions based on these representations and expansions. The use of these methods to solve constrained
least squares problems is examined.
Continued from Cybernetics and Systems Analysis, 44, No. 1, 36–55 (2008).
__________
Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 75–102, May–June 2008. 相似文献
5.
Limiting Representations of Weighted Pseudoinverse Matrices with Positive Definite Weights. Problem Regularization 总被引:2,自引:2,他引:0
Limiting representations for weighted pseudoinverse matrices with positive definite weights are derived. It is shown that regularized problems can be constructed based on such limiting representations intended for evaluation of weighted pseudoinverse matrices and weighted normal pseudosolutions with positive definite weights. The results obtained, concerning regularization of problems on evaluation of weighted normal pseudosolutions, are employed for regularization of least-squares problems with constraints. 相似文献
6.
The authors develop and analyze iterative methods with different (linear, quadratic, or of p (p2) order) rates of convergence. The methods are used to calculate weighted pseudoinverse matrices with positive defined weights. To find weighted normal pseudosolutions with positive defined weights, iterative methods with a quadratic rate of convergence are developed and analyzed. The iterative methods for calculation of weighted normal pseudosolutions are used to solve least-square problems with constraints.Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 20–44, September–October 2004. 相似文献
7.
The paper considers weighted pseudoinverse where both weighted matrices are symmetric and one of them is positive definite matrix and the other is nonsingular and indefinite. Formulas are obtained to represent these matrices in terms of the Moore–Penrose pseudoinverse matrix and other weighted pseudoinverses. 相似文献
8.
A weighted least squares problem {ie863-01} with positive definite weights M and N is considered, where A ∈ Rm×n is a rank-deficient matrix, b ∈ Rm. The hereditary, computational, and global errors of a weighted normal pseudosolution are estimated for perturbed initial
data, including the case where the rank of the perturbed matrix varies.
Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 83–95, November–December 2008. 相似文献
9.
The clustering of vector observations of hyperplanes is studied. Different cases of correspondence distances are proposed
and investigated, including the algebraic Jack Knife one. The efficiency, constructivity, and explicit form of formulas are
provided by using the pseudoinverse technique including the pseudoinverse-perturbation theory. Results important for the application
of pseudoinverse and related operators are presented.
__________
Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 73–92, July–August 2007. 相似文献
10.
E. F. Galba 《Cybernetics and Systems Analysis》1998,34(2):245-253
We construct iterative processes to compute the weighted normal pseudosolution with positive definite weights (weighted least
squares solutions with weighted minimum Euclidean norm) for systems of linear algebraic equations (SLAE) with an arbitrary
rectangular real matrix. We examine two iterative processes based on the expansion of the weighted pseudoinversc matrix into
matrix power series. The iterative processes are applied to solve constrained least squares problems that arise in mathematical
programming and to findL-pseudosolutions.
Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 116–124, March–April, 1998. 相似文献