Skip to Main Content
Book Chapter

Conjugate-Gradient and Quasi-Newton Methods

By
Published:
January 01, 2017

Abstract

Conjugate-Gradient and Quasi-Newton Methods: We now will discuss two gradient-optimization methods commonly used in geophysical inversion: the conjugate-gradient (CG) method and the quasi-Newton (QN) method. Unlike the Newton method, these two methods do not explicitly compute the inverse to the Hessian; instead, they iteratively move along descent directions that reduce the data residual. Each iteration costs only O(N2) operations of a matrix-vector multiply. Another strength is that, in the case of CG and low-memory QN methods, no Hessian matrix needs to be stored or inverted explicitly. Their weakness is that fast convergence is not guaranteed. However, they are generally faster than the nonpreconditioned steepest-descent method.

You do not currently have access to this article.

Figures & Tables

Contents

Society of Exploration Geophysicists

Seismic Inversion

Gerard T. Schuster
Gerard T. Schuster
Search for other works by this author on:
Society of Exploration Geophysicists
Volume
20
ISBN electronic:
9781560803423
Publication date:
January 01, 2017

GeoRef

References

Related

Citing Books via

A comprehensive resource of eBooks for researchers in the Earth Sciences

Close Modal
This Feature Is Available To Subscribers Only

Sign In or Create an Account

Close Modal
Close Modal