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On the solvability and numerical methods for solution of linear integro-algebraic equations

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Abstract

We study solvability conditions for a system of Volterra equations with some identically degenerate or rectangular matrix at the main term. Connection is discussed of the solvability conditions and applicability of numerical methods for solving these systems. In particular, the conditions of the convergence of the least squares method with the error functional defined in Sobolev spaces are presented.

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Authors and Affiliations

  1. Institute for System Dynamics and Control Theory, Irkutsk, Russia

    V. F. Chistyakov

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  1. V. F. Chistyakov
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Correspondence to V. F. Chistyakov.

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Original Russian Text Copyright © 2013 Chistyakov V.F.

The author was supported by the Russian Foundation for Basic Research (Grant 11-01-00639-a) and the Interdisciplinary Project of the Siberian Division of the Russian Academy of Sciences (No. 80).

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 54, No. 4, pp. 932–946, July–August, 2013.

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Chistyakov, V.F. On the solvability and numerical methods for solution of linear integro-algebraic equations. Sib Math J 54, 746–758 (2013). https://doi.org/10.1134/S0037446613040149

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  • DOI: https://doi.org/10.1134/S0037446613040149

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