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


  • A.A. Dryazhenkov Lomonosov Moscow State University




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


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.

Author Biography

A.A. Dryazhenkov


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How to Cite

Дряженков А.А. A Modified Generalized Residual Method for Minimization Problems With Errors of a Known Level in Weakened Norms // Numerical Methods and Programming (Vychislitel’nye Metody i Programmirovanie). 2015. 16. 456-463. doi 10.26089/NumMet.v16r443



Section 1. Numerical methods and applications