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National Repository of Grey Literature

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Golub-Kahan Iterative Bidiagonalization and Stopping Criteria in Ill-Posed Problems Hnětynková, Iveta ; Plešinger, Martin ; Strakoš, Zdeněk Detailed record

Lanczošova třídiagonalizace, Golub-Kahanova bidiagonalizace a core problém Hnětynková, Iveta ; Strakoš, Zdeněk Consider an orthogonally invariant linear approximation problem Ax ~ b. In "C.C. Paige, Z. Strakoš: Core problems in linear algebraic systems (SIAM J. Matrix Anal. Appl. 27 (2006), pp. 861-875)" it was proved that the partial upper bidiagonalization of the matrix [b,A] determines a core approximation problem that contains the necessary and sufficient information for solving the original problem. Our contribution derives the fundamental characteristics of the core problem from the known relationship between the Golub-Kahan bidiagonalization, the Lanczos tridiagonalization and the properties of Jacobi matrices. Detailed record

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