Krylov subspace accelerated inexact Newton method for linear and nonlinear equations.

A Krylov subspace accelerated inexact Newton (KAIN) method for solving linear and nonlinear equations is described, and its relationship to the popular direct inversion in the iterative subspace method [DIIS; Pulay, P., Chem Phys Lett 1980, 393, 73] is analyzed. The two methods are compared with application to simple test equations and the location of the minimum energy crossing point of potential energy surfaces. KAIN is no more complicated to implement than DIIS, but can accommodate a wider variety of preconditioning and performs substantially better with poor preconditioning. With perfect preconditioning, KAIN is shown to be very similar to DIIS. For these reasons, KAIN is recommended as a replacement for DIIS. Copyright 2003 Wiley Periodicals, Inc.