Explicit Pseudo-transient Continuation

We analyze and extend an explicit pseudo-transient continuation algorithm proposed by Han and Han. We present a convergence proof, extend the method to bound-constrained optimization, and proposed an improved step-size control strategy. 1. Introduction. The purpose of this paper is to analyze and extend an explicit version of pseudo-transient continuation (ΨTC) which has been proposed in [6] for nonlinear equations and in [7] for uncon-strained optimization. This method is appealing, as are all explicit methods, because it does not require solutions of linear systems. The disadvantage, of course, is that more iterations will be needed because the fast local convergence of Newton's method will be lost. In this introductory section we explain ΨTC , review some existing methods and describe the simplest version of the method from [6]. We follow that with the analysis and extensions, and finish the paper with a numerical example. The objective of the method of pseudo-transient continuation [4, 11, 12] is to integrate an initial value problem