Solving high-dimensional nonlinear equations with infinite solutions by the SVM visualization method

Abstract

There are many standard mathematical methods for solving nonlinear equations. But when it comes to equations with infinite solutions in high dimension, the results from current methods are quite limited. Usually these methods apply to differentiable functions only and have to satisfy some conditions to converge during the iteration. Even if they converge, only one single root is found at a time. However, using the features of SVM, we present a simple fast method which could tell the distribution of these infinite solutions and is capable of finding approximation of the roots with accuracy up to at least 10^−12 . In the same time, we could also have a visual understanding about these solutions.