共查询到10条相似文献,搜索用时 109 毫秒
1.
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
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.
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Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 32–62, January–February 2006. 相似文献
3.
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.
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Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 45–64, January–February 2007. 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).
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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 method of perturbation of pseudoinverse matrices, developed earlier by the authors based on splitting matrices, is extended to projective matrices for their further application to identification, nonlinear regressive analysis, function approximation, and prediction problems. 相似文献
8.
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.
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Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 73–92, July–August 2007. 相似文献
9.
The paper considers the synthesis of signal classification systems using the theory of perturbation of pseudoreverse and projection
matrices and proposes an algorithm to select (filter) separable subsets on a finite point set from R
n
.
Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 124–134, July–August 2009. 相似文献
10.
Optimal synthesis of linear and nonlinear transformations is used to synthesize pattern recognition systems. The necessary
and sufficient conditions for the existence of robust dichotomous linear separability of sets in feature space are represented
in terms of pseudoinverse operations. The synthesis of classification systems is reduced to searching for the best nonlinear
transformations of the components of the feature vector or optimal linear combinations of its components.
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Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 47–56, May–June 2007. 相似文献