标题： 快速收敛到高重数零点 显示英文标题

标题： Fast convergence to higher multiplicity zeros

摘要： 在本文中，通过将一种称为安德森加速的外推技术应用于牛顿法，得到的牛顿-安德森方法被证明在解析和数值上都能对标量方程的非简单根提供超线性收敛。 该方法既不需要事先知道根的重数，也不需要计算任何额外的函数值或导数。 显示英文摘要

摘要： 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.