Because of their versatility and robustness, numerical continuation or path following
methods have been finding ever wider use in scientific applications. Our aim here is to give …

The basic theory for probability one globally convergent homotopy algorithms was
developed in 1976, and since then the theory, algorithms, and applications have …

Over the past fifteen years two new techniques have yielded extremely important
contributions toward the numerical solution of nonlinear systems of equations. This book …

This book was intended as an introduction to the topic of numerical continuation which
would be accessible to a readership of widely varying mathematical backgrounds. Realizing …

This paper presents a digest of recently developed simplicial and continuation methods for
approximating fixed-points or zero-points of nonlinear finite-dimensional mappings …

The main ideas of path following by predictor–corrector and piecewise-linear methods, and
their application in the direction of homotopy methods and nonlinear eigenvalue problems …

Probability one homotopy algorithms are a class of methods for solving nonlinear systems of
equations that are globally convergent with probability one. These methods are theoretically …

Abstract The Chow-Yorke algorithm is a homotopy method that has been proved globally
convergent for Brouwer fixed-point problems, certain classes of zero finding and nonlinear …

This paper considers the problem of solving a system of n nonlinear equations in n
variables, when the underlying functions are continuously differentiable and their derivative …

Piecewise linear methods had their beginning in the mid-1960s with Lemke's algorithm for
calculating solutions to linear complementarity problems. In the 1970s and 1980s activity …