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A continuous regularization method for a constrained pseudoinverse problem with additional restrictions on the input operators

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Abstract

A two-parameter continuous regularization method is considered for a constrained pseudoinverse problem with input operators satisfying a generalized complementarity condition. The method is based on the stabilization of the solutions of differential equations in a Hilbert space. Convergence conditions refining those known previously are found. The main result is that the parameter functions are independent of each other. The stability of the method is established in the class of all possible constrained perturbations. A one-parameter continuous regularization method is studied for a special case of the problem with additional input operators.

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Authors and Affiliations

  1. Nizhny Novgorod State Pedagogical University, ul. Ul’yanova 1, Nizhny Novgorod, 603950, Russia

    R. A. Shafiev

  2. Nizhny Novgorod State University of Architecture, Building, and Civil Engineering, Il’inskaya ul. 65, Nizhny Novgorod, 603950, Russia

    E. A. Bondar

  3. Nizhny Novgorod State University, pr. Gagarina 23, Nizhny Novgorod, 603950, Russia

    I. Yu. Yastrebova

Authors
  1. R. A. Shafiev
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  2. E. A. Bondar
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  3. I. Yu. Yastrebova
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Corresponding author

Correspondence to R. A. Shafiev.

Additional information

Original Russian Text © R.A. Shafiev, E.A. Bondar, I.Yu. Yastrebova, 2016, published in Uchenye Zapiski Kazanskogo Universiteta, Seriya Fiziko-Matematicheskie Nauki, 2016, Vol. 158, No. 1, pp. 106–116.

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Shafiev, R.A., Bondar, E.A. & Yastrebova, I.Y. A continuous regularization method for a constrained pseudoinverse problem with additional restrictions on the input operators. Lobachevskii J Math 37, 807–814 (2016). https://doi.org/10.1134/S1995080216060020

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  • DOI: https://doi.org/10.1134/S1995080216060020

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