Formulas of perturbation for one class of pseudo
inverse operators

O. G. Nakonechniy; G. I. Kudin; T. P. Zinko

doi:10.30970/ms.52.2.124-132

Pseudo inverse matrix research, as well as related issue of their application, is in focus of scientific literature recently. Moreover, the field of applications of pseudo inverse matrices is expanding and obtained theoretical results are successfully used to solve practical problems. Interest in the pseudo inverse matric problem is large due to their various applications: in control theory, identification problems, approximation theory, statistical problems, theory of recurrent filtration and others. We investigate a linear operator equation, where the operator is a linear combination of matrices. We obtain solution using the pseudo inverse operation and small parameter method.

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3. Kirichenko N.F. An analytical representation of perturbations of pseudo inverse matrices// Cybernetics and system analysis. – 1997. – №2. – P. 98–107. (in Russian)

4. Kirichenko N.F., Donchenko V.S. Pseudo Reversal in the problems of clusterization// Cybernetics and System Analysis. – 2007. – №4. – P. 73–92. (in Russian)

5. Kirichenko N.F., Kudin G.I. Analysis and synthesis of systems of classification of signals by means of perturbations of pseudo inverse and projection operations// Cybernetics and system analysis. – 2009. – №3. – P. 47–57. (in Russian)

6. Kirichenko N.F., Kudin G.I. Variations of pseudo inverse and projection matrices with perturbation of elements of the original matrix// Problems of control and informatics. – 2009. – №3. – P. 7–20. (in Russian)

7. Donchenko V.S., Zinko T., Skotarenko F. ’Feature vectors’ in grouping information problem in applied mathematics: vectors and matrices// Problems of Computer Intellectualization, Kyiv: ITHEA, 2012. – P. 111–124.

8. Nayfe A.H. Introduction to perturbation methods. – M.: Mir, 1984. – 536 p. (in Russian)

9. Blokhintsev D.I. Fundamentals of Quantum Mechanics. – M .: Nauka, 1976. – 864 p. (in Russian)

	Formulas of perturbation for one class of pseudo inverse operators
Author	O. G. Nakonechniy¹, G. I. Kudin², T. P. Zinko³ a.nakonechniy@gmail.com¹, gkudin@ukr.net², taras.zinko@gmail.com³ Taras Shevchenko National University of Kyiv, Kyiv, Ukraine
Abstract	Pseudo inverse matrix research, as well as related issue of their application, is in focus of scientific literature recently. Moreover, the field of applications of pseudo inverse matrices is expanding and obtained theoretical results are successfully used to solve practical problems. Interest in the pseudo inverse matric problem is large due to their various applications: in control theory, identification problems, approximation theory, statistical problems, theory of recurrent filtration and others. We investigate a linear operator equation, where the operator is a linear combination of matrices. We obtain solution using the pseudo inverse operation and small parameter method.
Keywords	vector decomposition; pseudo inverse; linear operator; SVD; perturbed operator
DOI	doi:10.30970/ms.52.2.124-132
Reference	1. Albert A. Regression, pseudo inverse, recurrent evaluation. – M .: Nauka, 1977. – 305 p. (in Russian) 2. Cline R.E. Representation for the generalized inverse of partitioned matrix// SIAM J. Appl. Math. – 1964. – V.32. – P. 588–600. 3. Kirichenko N.F. An analytical representation of perturbations of pseudo inverse matrices// Cybernetics and system analysis. – 1997. – №2. – P. 98–107. (in Russian) 4. Kirichenko N.F., Donchenko V.S. Pseudo Reversal in the problems of clusterization// Cybernetics and System Analysis. – 2007. – №4. – P. 73–92. (in Russian) 5. Kirichenko N.F., Kudin G.I. Analysis and synthesis of systems of classification of signals by means of perturbations of pseudo inverse and projection operations// Cybernetics and system analysis. – 2009. – №3. – P. 47–57. (in Russian) 6. Kirichenko N.F., Kudin G.I. Variations of pseudo inverse and projection matrices with perturbation of elements of the original matrix// Problems of control and informatics. – 2009. – №3. – P. 7–20. (in Russian) 7. Donchenko V.S., Zinko T., Skotarenko F. ’Feature vectors’ in grouping information problem in applied mathematics: vectors and matrices// Problems of Computer Intellectualization, Kyiv: ITHEA, 2012. – P. 111–124. 8. Nayfe A.H. Introduction to perturbation methods. – M.: Mir, 1984. – 536 p. (in Russian) 9. Blokhintsev D.I. Fundamentals of Quantum Mechanics. – M .: Nauka, 1976. – 864 p. (in Russian)
Pages	124-132
Volume	52
Issue	2
Year	2019
Journal	Matematychni Studii
Full text of paper	pdf
Table of content of issue	html

Formulas of perturbation for one class of pseudo inverse operators