Computational and Applied Math Proseminar

Thursday, March 20, 12:15 p.m. PSA 206

Iveta Hnetynkova

Dept Math & Stats

Noise-Revealing Golub-Kahan Bidiagonalization with
Application in Hybrid Methods

Abstract
Regularization techniques based on Golub-Kahan bidiagonalization have been used for the iterative solution 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 inner regularization and parameter selection method, e.g. L-curve, the discrepancy principle, or generalized cross validation, is applied to it. This also leads to a decision when it is optimal to stop the bidiagonalization.

Recently, it has been proved that the Golub-Kahan bidiagonalization leads to a fundamental decomposition of data, revealing the so-called core problem. Applications to ill-posed problems have been studied by D. Sima, S. Van Huffel, P.C. Hansen, etc.

In this contribution we consider an ill-posed problem with noisy right-hand side and study how the noise in the data enters the projected problem obtained by the bidiagonalization. We investigate a possibility of directly using this information for constructing an effective stopping criterion in solving ill-posed problems.

For further information please contact: mittelmann@asu.edu