Lanczos Tridiagonalization and Core Problems

• ID: 2395, RIV: 10030483
• ISSN: 0024-3795, ISBN: not specified
• source: Linear Algebra and its Applications
• keywords: Lanczos; Tridiagonalization; Problems
• authors: Iveta Hnětynková, Zdeněk Strakoš
• authors from KNM: Strakoš Zdeněk, Hnětynková Iveta

Abstract

The paper 'C.C. Paige, Z. Strakoš: Core problems in linear algebraic systems (SIAM J. Matrix Anal. Appl. 27 (2006), pp. 861-875)' presents a core problem formulation of orthogonally invariant linear approximation problems Ax ~ b, that extracts 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 and the Lanczos tridiagonalization.