Lanczos Tridiagonalization and Core Problems

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.

Keywords

• Lanczos
• Tridiagonalization
• Problems