Homotopy algorithms and properties of systems of polynomial equations

Forster, Walter (1997) Homotopy algorithms and properties of systems of polynomial equations. In Proceedings of ISMP 97: International Symposium on Mathematical Programming. Mathematical Programming Society. pp. 24-32 .

Abstract

Homotopy algorithms combine beautiful mathematics with the capability to solve complicated nonlinear systems. Developed over the last 30 years, these algorithms have shown to be capable of solving problems where other algorithms fail. The algorithm given by Kuhn for a polynomial in one variable finds all the roots of a polynomial of degree n . A problem encountered in the convergence proof for the case of multiple roots was resolved by W.Forster in 1992 by using material from Nielsen fixed point theory. This then opened the way for the determinination of the number of solution classes for systems of polynomial equations in more than one variable. In the talk the number of solution classes for systems of polynomial equations will be discussed. We will also discuss the influence this has on the solution of the Kuhn-Tucker equations by homotopy methods.

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