A preconditioned Krylov subspace method for the solution of least squares problems in inverse scattering
The paper concerns the solution of large least squares (LS) problems by means of iterative methods. It starts with a brief survey of well-known methods such as SIRT, ART, CG, etc. Then, the authors present two preconditioned Krylov subspace methods to solve undetermined LS problems. They show that one of the methods has no breakdown and that the other is more efficient. To analyze the convergence behavior, a relation between the residual error and the eigenvalues of the preconditioned matrix is presented. As an important application of their method the authors consider an example arising in seismic scattering. In this case, under reasonable assumptions on the data, the authors are able to obtain a suitable preconditioner from the high-frequency asymptotics of the underlying problem. The derivation of such preconditioner is presented in the appendix. The paper concludes with a careful numerical comparison among the results obtained by applying their methods and other ones insofar as rate of convergence is concerned. The experiments indicate that the proposed preconditioned Krylov methods are three times faster than conjugate gradient for the large seismic examples under consideration.
scientific article; zbMATH DE number 881857