Lanczos Tridiagonalization, Golub-Kahan Bidiagonalization and the Core Problem

• ID: 2315, RIV: 10032003
• ISSN: neuvedeno, ISBN: neuvedeno
• zdroj: Modelling and Simulation of Challenging Engineering Problems
• klíčová slova: Lanczos; Tridiagonalization; Golub-Kahan; Bidiagonalization; Problem
• autoři: Iveta Hnětynková, Zdeněk Strakoš
• autoři z KNM: Strakoš Zdeněk, Hnětynková Iveta

Abstrakt

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.