A Method to Solve Systems of Nonlinear Equations with Singularities
R. Schulze · ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik · 1987
Abstract We investigate a fast‐convergent derivation‐free method for computing zeros of systems of nonlinear equations with singularities which, in general, needs fewer assumptions than the Newton‐like methods applied usually, and which has proved to be highly efficient by lots of examples. First we transform an arbitrary zero problem into an equivalent, in general under‐determined, zero problem. Then we consider a possibility to transform a zero problem into a possibly globally convergent fixed point form by means of a suitable matrix. We show several possibilities to characterize this matrix. Since the pure Banach iteration provides only linear convergence order of the iterated sequence, we speed up the procedure by means of limit value extrapolation so that we finally obtain a quadratic order of convergence.