Construction of iteration functions for the simultaneous computation of the solutions of equations and algebraic systems
The author constructs Newton-like iteration methods for the real solutions of systems of algebraic equations. The methods considered are related to and generalize the methods of Durand and Kerner for the calculation of all real roots of univariate polynomials via, e.g., the symmetric equations for the roots of a polynomial. Analogous resolvent systems are formulated and the iteration maps for such systems are simplified Newton maps. Local quadratic convergence results are given. Several numerical examples are also given. It would be of interest to compare the performance of the present method with the recently developed homotopy continuation methods for this class of problems.
scientific article; zbMATH DE number 553668