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Zh. Vychisl. Mat. Mat. Fiz., 2009, Volume 49, Number 10, Pages 1757–1764 (Mi zvmmf4766)  

This article is cited in 1 scientific paper (total in 1 paper)

Gradient projection method for stable approximation of quasisolutions to irregular nonlinear operator equations

A. I. Kozlov, M. Yu. Kokurin

Mari State University, pl. Lenina 1, Yoshkar-Ola, 424001, Russia

Abstract: An iterative process of the gradient projection type is constructed and examined as a tool for approximating quasisolutions to irregular nonlinear operator equations in a Hilbert space. One step of this process combines a gradient descent step in a finite-dimensional affine subspace and the Fejrér operator with respect to the convex closed set to which the quasisolution belongs. It is proved that the approximations generated by the proposed method stabilize in a small neighborhood of the desired quasisolution, and the diameter of this neighborhood is estimated.

Key words: irregular nonlinear operator equations, quasisolution, iterative methods, convergence, stability.

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English version:
Computational Mathematics and Mathematical Physics, 2009, 49:10, 1678–1685

Bibliographic databases:

UDC: 519.642.8
Received: 22.12.2008

Citation: A. I. Kozlov, M. Yu. Kokurin, “Gradient projection method for stable approximation of quasisolutions to irregular nonlinear operator equations”, Zh. Vychisl. Mat. Mat. Fiz., 49:10 (2009), 1757–1764; Comput. Math. Math. Phys., 49:10 (2009), 1678–1685

Citation in format AMSBIB
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\by A.~I.~Kozlov, M.~Yu.~Kokurin
\paper Gradient projection method for stable approximation of quasisolutions to irregular nonlinear operator equations
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2009
\vol 49
\issue 10
\pages 1757--1764
\mathnet{http://mi.mathnet.ru/zvmmf4766}
\transl
\jour Comput. Math. Math. Phys.
\yr 2009
\vol 49
\issue 10
\pages 1678--1685
\crossref{https://doi.org/10.1134/S0965542509100030}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-76349104412}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Kokurin M.Y., “Stable gradient projection method for nonlinear conditionally well-posed inverse problems”, J. Inverse Ill-Posed Probl., 24:3 (2016), 323–332  crossref  mathscinet  zmath  isi  elib  scopus
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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