H-非线性方程组的一种高效迭代解法

１．引言满足参见（［５］）（１．１）的任一非线性刚性函数ｆ（ｙ）：所产生的非线性方程组称之为由 ｆ（ｙ）产生的 Ｈ－非线性方程组，其中 Ａ，Ａ１为与 ｆ（ｙ）的刚性无关的常数，最多为中等大小；的第ｉ个特征值；常数，或者ｖ＞０且最多为中等大小；所谓“中等大小”是指与。相比较而言的；显然，已知；ａ，ｂ，ｃ，ｄ满足且均为常数，（１．２）是由混合（Ｈｙｂｒｉｄ）法解初值问题导出的，其中 ｈ是积分步长．对ｋ１＝ １，即所谓一阶刚性初值问题，混合法已有诸多研究（见［６，９－１１，１４－１６］）；对 ｋ１＝ ２，即所…

A HIGH EFFICIENCY ITERATIVE SOLUTION METHOD FOR H-NONLINEAR EQUATION SYSTEMS

For the H-nonlinear equation systems produced by stiffnonlinear function f(y): y Rm Rm, the paper presents a new Newton-like iterative solution method:completely-square method, establishes its convergence theory and offersfour simple algorithms for approximate calculation of optimum iterativeparameter in this method. The iterative method do not need tocompute(f)2, and LU-decomposition only need to be done forsome m m matrix. Numerical examples show that if appropriateapproximate optimum iterative parameter is selected on the coefficientsin the hybrid method that products the H-nonlinear equation systems then theiterative solution method in the paper is high efficieney.