关于奇异非线性方程组求解的Euler方法的收敛性

Convergence Criteria of Euler's Method about the Singular Nonlinear Systems of Equations

Banach空间中的非线性算子方程F(y)=0的求解是计算数学的理论基础,也是现代科学计算的核心问题之一.求解方程的算法比较重要的有Euler方法.该文在Lipschitz条件下,研究了求奇异非线性方程组的解的Euler方法的收敛问题,并给出了Euler迭代序列收敛于方程组解的判据.

Solving nonlinear operator equation in Banach space is the core issue of modern computational mathematics and the theoretical basis of calculation-rrealizing. The primary means to solve such problem is Euler＇s method. This paper researches on the convergence problem of Euler＇s method to find the solutions of the singular nonlinear systems of equations under the Lipschitz condition, and presents the criterion of the iterative sequence converge to the solution of the equations.