Contraction, Robustness, and Numerical Path-Following Using Secant Maps

AbstractSecant type methods are useful for finding zeros of analytic equations that include polynomial systems. This paper proves new results concerning contraction and robustness theorems for secant maps. It is also shown that numerical path-following using secant maps has the same order of complexity that numerical path-following using Newton's map to approximate a zero. Such an algorithm was implemented and some numerical experiments are displayed