A globally convergent method for finding zeros of smooth functions

摘要

Computing a zero of a smooth function is an old and extensively researched problem in numerical computation. While a large body of results and algorithms has been reported on this problem in the literature, to the extent we are aware, the published literature does not contain a globally convergent1 algorithm for finding a zero of an arbitrary smooth function. In this paper we present the first globally convergent algorithm for computing a zero (if one exists) of a general smooth function. After presenting the algorithm and a proof of global convergence, we also clarify the connection between our algorithm and some known results in topological degree theory.