Fractional Tikhonov regularization for linear discrete ill-posed problems

• DOI: 10.1007/s10543-011-0313-9
• Publication Date: 2011-02-07T08:38:07Z
• Authors: Michiel E. Hochst...; Lothar Reichel
• Keywords: Backus–Gilbert method; Moore–Penrose pseudoinverse; Regularization; Well-posed problem

Tikhonov regularization is one of the most popular methods for solving linear systems equations or least-squares problems with a severely ill-conditioned matrix A. This method replaces given problem by penalized problem. The present paper discusses measuring residual error (discrepancy) in seminorm that uses fractional power Moore-Penrose pseudoinverse AA T as weighting matrix. Properties this are discussed. Numerical examples illustrate proposed scheme suitable may give approximate solutions higher quality than standard regularization.