A preconditioned Krylov subspace method for the solution of least squares problems in inverse scattering
type: Item
instance of: scholarly article
title: A preconditioned Krylov subspace method for the solution of least squares problems in inverse scattering
zbMATH Open document ID: 0857.65044
author: Agur G. J. Sevink
author: Gérard C. Herman
author: C. Vuik
published in: Journal of Computational Physics
publication date: 1996-07-02T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 65F20
Mathematics Subject Classification ID: 65F35
Mathematics Subject Classification ID: 35Q72
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 86A22
Mathematics Subject Classification ID: 86A15
zbMATH DE Number: 881857
zbMATH Keywords: inverse scattering
zbMATH Keywords: large least squares problems
zbMATH Keywords: iterative methods
zbMATH Keywords: preconditioned Krylov subspace methods
zbMATH Keywords: convergence
zbMATH Keywords: seismic scattering
zbMATH Keywords: numerical comparison
zbMATH Keywords: conjugate gradient
reviewed by: J. P. Zubelli
MaRDI profile type: Publication
full work available at URL: jcph.1996.0027
OpenAlex ID: W2106158414
DOI: 10.1006/JCPH.1996.0027
description: scientific article; zbMATH DE number 881857