H-非线性方程组的一种高效迭代解法  

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

作　　者：赵双锁[1] 张新平[2] 

机构地区：[1]西北第二民族学院信息与计算科学系,银川750021 [2]武汉邮电科学研究院,武汉430074

出　　处：《计算数学》2000年第4期417-428,共12页Mathematica Numerica Sinica

基　　金：国家自然科学基金

摘　　要：For the H-nonlinear equation systems produced by stiff nonlinear function f(y): y ∈ Rm→Rm, the paper presents a new Newton-like iterative so- lution method: completely-square method, establishes its convergence theory and offers four simple algorithms for approximate calculation of optimum iterative pa- rameter in this method. The iterative method do not need to compute(f’)2, and LU-decomposition only need to be done for some m × m matrix. Numerical examples show that if appropriate approximate optimum iterative parameter is selected on the coefficients in the hybrid method that products the H-nonlinear equation systems then the iterative solution method in the paper is high efficiency.For the H-nonlinear equation systems produced by stiff nonlinear function f(y): y ∈ Rm→Rm, the paper presents a new Newton-like iterative so- lution method: completely-square method, establishes its convergence theory and offers four simple algorithms for approximate calculation of optimum iterative pa- rameter in this method. The iterative method do not need to compute(f')2, and LU-decomposition only need to be done for some m × m matrix. Numerical examples show that if appropriate approximate optimum iterative parameter is selected on the coefficients in the hybrid method that products the H-nonlinear equation systems then the iterative solution method in the paper is high efficiency.

关 键 词：H-非线性方程组 迭代解法 收敛性 守全平方迭代法 微分方程组 

分 类 号：O241[理学—计算数学]