On Continuous Regularization Method for a Constrained Pseudoinverse Problem with Additional Restrictions on Input Operators

• Main Authors: R.A. Shafiev, E.A. Bondar, I.Yu. Yastrebova
• Format: Article
• Language: Russian
• Published: Kazan Federal University 2016-03-01
• Series: Učënye Zapiski Kazanskogo Universiteta: Seriâ Fiziko-Matematičeskie Nauki
• Subjects: normal constrained pseudosolution; operator equation; Hilbert space; constrained pseudoinverse problem; continuous method of regularization; generalized complementarity condition of operators; complementarity condition of operators
• Online Access: http://kpfu.ru/portal/docs/F1518090557/158_1_phys_mat_8.pdf

A two-parameter continuous method of regularization is considered for a constrained pseudoinverse problem with generalized complementarity of the input operators. This method is based on stabilization of the solutions of differential equations in the Hilbert space. The already known general convergence conditions are specified. The major obtained result is that the parameter functions proved to be independent from each other. The stability of the method is established in the class of all possible constrained disturbances. A one-parameter continuous method of regularization is studied for the special case of the problem with additional input operators.