Golub-Kahan iterative bidiagonalization and stopping criteria in ill-posed problems

Abstract

Golub-Kahan bidiagonalization has been used for iterative solving of large ill-posed problems for years. First, the original problem is projected onto a lower dimensional subspace using the bidiagonalization algorithm and then some type of regularization is used on it.

This also leads to the decision when it is optimal to stop the bidigonalization. In this contibution we investigate a possibility of direct using of the information from the bidiagonalization for process constructing an effective stopping criteria in solving ill-posed problems.

Keywords

• Golub-Kahan
• iterative
• bidiagonalization
• stopping
• criteria
• ill-posed
• problems