Parallel homotopy algorithms

Abstract

Algorithms for solving nonlinear systems of equations can be broadly classified as (1) locally convergent or (2) globally convergent. The former includes Newton's method, various quasi-Newton methods, and inexact Newton methods. The latter includes continuation, simplicial methods, and probability-one homotopy methods. These algorithms are qualitatively significantly different, and their relative performance on parallel systems may very well be the reverse of their performance on serial processors.