TY - JOUR
T1 - Tikhonov Regularization and Total Least Squares
JF - SIAM Journal on Matrix Analysis and Applications
Y1 - 1999
A1 - Golub, Gene H.
A1 - Hansen,Per Christian
A1 - O'Leary, Dianne P.
KW - bidiagonalization
KW - discrete ill-posed problems
KW - regularization
KW - total least squares
AB - Discretizations of inverse problems lead to systems of linear equations with a highly ill-conditioned coefficient matrix, and in order to computestable solutions to these systems it is necessary to apply regularization methods. We show how Tikhonov's regularization method, which in its original formulation involves a least squares problem, can be recast in a total least squares formulation suited for problems in which both the coefficient matrix and the right-hand side are known only approximately. We analyze the regularizing properties of this method and demonstrate by a numerical example that, in certain cases with large perturbations, the new method is superior to standard regularization methods.
VL - 21
UR - http://link.aip.org/link/?SML/21/185/1
CP - 1
M3 - 10.1137/S0895479897326432
ER -