On the preconditioning of the bidiagonalization technique

Abstract

Two algorithms derived by Paige (1974), to solve the linear least squares problems based on Golub and Kahan's bidiagonalization algorithm to reduce a general matrix to a bidiagonal form.

A preconditioning of the bidiagonalization algorithm is shown to be very effective to improve the rate of convergence of the bidiagonalization algorithm with a general application to solve a nonlinear system with non-symmetric Jacobian by linearization.

Two preconditioning algorithms have been proposed, a comparison taken place to prove the efficiency of these algorithms.

Keywords:

• Preconditioning
• conjugate gradient method
• bidiagonalization technique
• sparse linear system

C.R.Categories:

• G1.3