A modified truncated singular value decomposition method for discrete ill-posed problems

Abstract

SUMMARY Truncated singular value decomposition is a popular method for solving linear discrete ill-posed problems with a small to moderately sized matrix A. Regularization is achieved by replacing the matrix A by its best rank-k approximant, which we denote by Ak. The rank may be determined in a variety of ways, for example, by the discrepancy principle or the L-curve criterion. This paper describes a novel regularization approach, in which A is replaced by the closest matrix in a unitarily invariant matrix norm with the same spectral condition number as Ak. Computed examples illustrate that this regularization approach often yields approximate solutions of higher quality than the replacement of A by Ak.Copyright © 2014 John Wiley & Sons, Ltd.