求解非线性算子方程的加速迭代格式

Accelerative Iterative Formula for the Non-linear Operator Equation

研究非线性算子方程的近似求解方法.首先对通常的求解非线性方程加速迭代格式进行推广,得到高阶收敛速度的加速迭代格式,最后把这种加速迭代格式推广到非线性算子方程的求解中去,利用非线性算子的渐进展开,证明了这种加速格式具有三阶的收敛速度.

Approximate solving method for the non-linear operator equation is investigated in this paper.First,we generalize the accelerative iterative formula of the non-linear functional equation so that we obtain the high-speed convergent iterative formula.Finally,the new accelerative iterative formula has been generalized for the non-linear operator equation.Using the asymptotic expansions of the non-linear operator,we prove that the new accelerative iterative formula is convergence with order 3.