The Use and Properties of Tikhonov Filter Matrices

Abstract

We consider the concept of Tikhonov filter matrices in connection with discrete ill-posed and rank-deficient linear problems. Important properties of the Tikhonov filter matrices are given together with their filtering and regularization effects. We also present new perturbation identities for the Tikhonov regularized linear least squares problem using filter matrices generalizing well-known perturbation identities for the linear least squares problem and pseudoinverses.