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Numerical methods and programming, 2015, Volume 16, Issue 4, Pages 456–463
(Mi vmp555)
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This article is cited in 1 scientific paper (total in 1 paper)
A modified generalized residual method for minimization problems with errors of a known level in weakened norms
A. A. Dryazhenkov Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics
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 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.
Keywords:
ill-posed problem, quadratic minimization, ellipsoid, approximate data, generalized residual method.
Received: 11.07.2015
Citation:
A. A. Dryazhenkov, “A modified generalized residual method for minimization problems with errors of a known level in weakened norms”, Num. Meth. Prog., 16:4 (2015), 456–463
Linking options:
https://www.mathnet.ru/eng/vmp555 https://www.mathnet.ru/eng/vmp/v16/i4/p456
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Abstract page: | 110 | Full-text PDF : | 42 |
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