Discretizations of inverse problems lead to systems of linear equations with
a highly ill-conditioned coefficient matrix, and in order to compute stable
solutions to these systems it is necessary to apply regularization methods.
We show how Tikhonov's regularization method, which in its original formu-
lation 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 regu-
larizing 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.
IMM Technical Report 15/97
Last modified April 21, 1997
For further information, please contact, Finn Kuno
Christensen, IMM, Bldg. 321, DTU Phone: (+45) 4588 1433. Fax: (+45) 4588
2673, E-mail: fkc@imm.dtu.dk
