超线性收敛的指数下降迭代法

摘要

This paper develops an iterative method of exponential descent with superlinear linear convegence x n+1 =x n exp (-f n(x n-x n-1 )/x n(f n-f n-1 )), x n≠0 for solving nonlinear equations. It becomes the well known secant method when we take linear approximation of the exponential function in the iterative method. Numerical tests show that exponential descent method has the advantage of secant method.