DOI: https://doi.org/10.26089/NumMet.v16r443

A modified generalized residual method for minimization problems with errors of a known level in weakened norms

Authors

  • A.A. Dryazhenkov

Keywords:

ill-posed problem
quadratic minimization
ellipsoid
approximate data
generalized residual method

Abstract

An algorithm is proposed for the numerical solution of a quadratic minimization problem on an ellipsoid specified in the Hilbert space by a compact operator. This algorithm is a certain transform of the generalized residual method designed previously for the application in nonclassical information conditions when {it a priori} information on the error level in an operator defining the cost functional is available only in the norms being weaker than the original ones. At the same time, the convergence of the algorithm is proved in the original norms. A number of simple numerical examples are discussed.

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Published

2015-08-17

Issue

Vol. 16 (2015): Issue 4.

Section

Section 1. Numerical methods and applications

Author Biography

A.A. Dryazhenkov

Lomonosov Moscow State University,
Faculty of Computational Mathematics and Cybernetics
• PhD Student

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