Original title: Lanczos Tridiagonalization, Golub-Kahan Bidiagonalization and the Core Problem
Translated title: Lanczošova třídiagonalizace, Golub-Kahanova bidiagonalizace a core problém
Authors: Hnětynková, Iveta ; Strakoš, Zdeněk
Document type: Papers
Conference/Event: SNA '06. Seminar on Numerical Analysis, Monínec (CZ), 2006-01-16 / 2006-01-20
Year: 2006
Language: eng
Abstract: [eng] [cze]
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. Uvažujme ortogonálně invariantní lineární aproximační problém Ax ~ b. V článku "C.C. Paige, Z. Strakoš: Core problems in linear algebraic systems (SIAM J. Matrix Anal. Appl. 27 (2006), pp. 861-875)" je dokázáno, že částečná horní bidiagonalizace matice [b,A] vede na tzv. core aproximační problém, který obsahuje nutné a postačující informace pro řešení původní úlohy. V tomto příspěvku odvodíme základní vlastnosti core problému ze známých vztahů mezi Golub-Kahanovou bidiagonalizací, Lanczošovou třídiagonalizací a vlastnostmi Jacobiho matic.
Keywords: core problem; Golub-Kahan bidiagonalization; Jacobi matrix; Lanczos tridiagonalization; linear approximation problem
Project no.: CEZ:AV0Z10300504 (CEP), 1ET400300415 (CEP)
Funding provider: GA AV ČR
Host item entry: Modelling and Simulation of Challenging Engineering Problems

Institution: Institute of Computer Science AS ČR (web)
Document availability information: Fulltext is available at the institute of the Academy of Sciences.
Original record: http://hdl.handle.net/11104/0132882

Permalink: http://www.nusl.cz/ntk/nusl-35317


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