关键词: 非线性方程, 参数估计, 最优化, 缩张算法, 数值微分, 程序

Abstract:

The improved contraction-expansion algorithm was established mainly by combining previous C-E algorithm with Levenberg-Marquardt method based on numerical derivative technique. The new algorithm could use differential information to guide searching direction without providing derivatives, so as to simplify fitting process and raise searching efficiency. The new C-E algorithm greatly reduced computing load for those multiple parameters situation and strengthened the ability to jump out off pitfalls. The feedback system was more sensitive than previous one in using scatter-spread of the spring points to adjust search step length. Improved effects were obtained in fitting various nonlinear equations with new algorithm. Some examples were given to demonstrate the power in curve and surface fitting.

Key words: Nonlinear equation, Parameter estimation, Optimization, Contraction-expansion algorithm, Numerical differentiation, Program