Spherical Continuation Algorithm with Spheres of Variable Radius to Trace Homotopy Curves

The homotopy continuation methods are capable to locate multiple solutions of nonlinear systems of equations. In this paper is presented the path-following technique used to trace the homotopy trajectory. The spherical method is employed resizing the radius of the sphere at each iteration, the above based on the behavior of the radius of curvature. Also the Newton homotopy is applied in conjunction with the proposed methodology for tracing homotopy curve. To prove the usefulness of the proposed method is applied to three examples with different numbers of equations obtaining successful results.