Fast convergence to higher multiplicity zeros

Abstract

In this paper, the Newton-Anderson method, which results from applying an extrapolation technique known as Anderson acceleration to Newton's method, is shown both analytically and numerically to provide superlinear convergence to non-simple roots of scalar equations. The method requires neither a priori knowledge of the multiplicities of the roots, nor computation of any additional function evaluations or derivatives.

3 tables, 1 figure