Preconditioned Krylov Subspace Method for the Solution of Least Squares Problems

摘要

We present an iterative method of preconditioned Krylov type for the solution oflarge least squares problems. We prove that the method is robust and investigate its rate of convergence. For an important application, originating from seismic inverse scattering, we derive a suitable preconditioner using asymptotic theory. Numerical experiments are used to compare the method with other iterative methods. It appears that the preconditioned Krylov method can be much more efficient than CG (Conjugate Gradients) applied to the normal equations. (Copyright (c) 1994 by Faculty of Technical Mathematics and Informatics, Delft, The Netherlands.)