Lanczos Tridiagonalization, Golub-Kahan Bidiagonalization and Core Problem

Abstract

Consider an orthogonally invariant linear approximation problem Ax ~ b. C.C.

Paige and Z. Strakoš proved that the partial upper bidiagonalization of the matrix [b,A] determines a core approximation problem that contains all necessary and sufficient information for solving the original problem.

I. Hnětynková and Z.

Strakoš derived the core problem formulation from the relationship between the Golub-Kahan bidiagonalization and the Lanczos tridiagonalization. Here we briefly recall this approach and outline a possible direction for further research.

Keywords

• Lanczos
• Tridiagonalization
• Golub-Kahan
• Bidiagonalization
• Problem