Chebyshev Subdivision and Reduction Methods for Solving Multivariable Systems of Equations
- Tyler Jarvis
Abstract
I present a new algorithm and Python implementation, YRoots, for finding isolated zeros of a system of real-valued smooth (not necessarily polynomial) functions in a bounded interval in R^n. It uses the Chebyshev proxy method combined with a mixture of subdivision, reduction methods, and elimination checks that leverage special properties of Chebyshev polynomials. The method has quadratic convergence locally near simple zeros of the system. It also finds all nonsimple zeros, but convergence to those zeros is not guaranteed to be quadratic.
Numerical evidence demonstrates that the method is both fast and accurate on a wide range of problems, significantly outperforming other standard methods on the problem of finding all real zeros in a bounded domain.
See paper at arxiv.org.
See the code on Github.
