On the Numerical Method of Following Homotopy Paths

In this paper, we develop one kind of method, called self-adaptive method (SAM), to trace a continuous curve of a homotopy system for the solution of a nonlinear system of equations in finite steps. The existence of the continuous solution, the determination of safe initial points, and the test of regularity and stop criterion corresponding to this method are discussed. As a result, the method can follow the curve efficiently. The numerical results show that our method is satisfactory.