Structure variable homotopy methods for solving nonlinear systems

摘要

This paper is devoted to the study of structure variable homotopy methods for solving nonlinear systems. A general structure variable homotopy algorithm is described in Section 2 and its relation with Newton's method is indicated. It is proved that a modified structure variable homotopy algorithm, called the descent structure variable homotopy, or DSVH, algorithm, converges globally and quadratically in the neighborhood of the solution under the hypothesis of the nonsingularity of the nonlinear systems. In Section 4, another structure variable homotopy algorithm is developed and the global convergence is also given. Finally, three numerical examples are given to demonstrate the effectiveness of our algorithms.