Newton iterative methods for large scale nonlinear systems. Final report, August 1992--July 1994

Abstract

Newton iterative methods, also known as truncated Newton methods, are implementations of Newton`s method in which an iterative linear solver is used to solve approximately the linear systems that characterize Newton steps. These methods are particularly appropriate for large-scale problems in which iterative linear algebra methods are preferred. They are currently used in many important scientific applications, including many of major industrial importance. In addition to their effectiveness on important problems, these methods also offer a nonlinear `framework` within which to transfer to the nonlinear setting any advances in linear system solving, such as new iterative methods for nonsymmetric linear systems, new preconditioning techniques, or new algorithms that exploit advanced machine architectures.