An Algorithm for Finding All Solutions of Parameter-Dependent Nonlinear Equations with Guaranteed Accuracy

摘要

This paper proposes an algorithm which can derive all solutions with guaranteed accuracy for equations include- ing a nonlinear function, with the dimension of the domain larger than the dimension of the range. It is mathematically shown that the proposed algorithm is completed in a finite number of steps under an appropriate condition. The effec- tiveness of the proposed algorithm is demonstrated by numerical examples.