## Continuation and Path Following (1992)

Citations: | 70 - 6 self |

### BibTeX

@MISC{Allgower92continuationand,

author = {Eugene L. Allgower and Kurt Georg},

title = {Continuation and Path Following},

year = {1992}

}

### Years of Citing Articles

### OpenURL

### Abstract

CONTENTS 1 Introduction 1 2 The Basics of Predictor-Corrector Path Following 3 3 Aspects of Implementations 7 4 Applications 15 5 Piecewise-Linear Methods 34 6 Complexity 41 7 Available Software 44 References 48 1. Introduction Continuation, embedding or homotopy methods have long served as useful theoretical tools in modern mathematics. Their use can be traced back at least to such venerated works as those of Poincar'e (1881--1886), Klein (1882-- 1883) and Bernstein (1910). Leray and Schauder (1934) refined the tool and presented it as a global result in topology, viz., the homotopy invariance of degree. The use of deformations to solve nonlinear systems of equations Partially supported by the National Science Foundation via grant # DMS-9104058 y Preprint, Colorado State University, August 2 E. Allgower and K. Georg may be traced back at least to Lahaye (1934). The classical embedding methods were the