Regularization Method by Rank Revealing QR Factorization and Its Optimization

Abstract

Tikhonov regularization using SVD (Singular Value Decomposition) is an effective method for discrete ill-posed linear operator equations. We propose a new regularization method using Rank Revealing QR Factorization which requires far less computational cost than that of SVD. It is important to choose regularization parameter to obtain a good approximate solution for the equation. For the choice of the regularization parameter, Generalized cross-validation (GCV) and the L-curve method are often used. We apply these two methods to the regularization using rank revealing QR factorization to produce a reasonable solution.