非线性不适定问题一种双循环的牛顿型迭代格式  

ON A NEWTON-TYPE METHOD FOR THE REGULARIZATION OF NONLINEAR ILL-POSED PROBLEMS

作　　者：张瑰[1] 黄思训[2] 

机构地区：[1]解放军理工大学理学院数理系,南京211101 [2]解放军理工大学气象学院军事气象系,南京211101

出　　处：《数学年刊（A辑）》2003年第3期321-330,共10页Chinese Annals of Mathematics

基　　金：国家自然科学基金(NO.40075014)

摘　　要：本文研究非线性算子方程F(x)=y的解,结合最速下降法,Newton-Landweber迭代格式及正则化思想,在F满足适当的条件下,构造出新的双循环迭代格式。本文对格式的收敛性进行了严格论证,并估计出迭代格式的收敛精度。This paper considers a Newton-type method, for regularizing the abstract nonlinear ill-posed operator equation F(x) = y. Under certain smoothness conditions on the nonlinear operator, the authors obtain the local convergence of the method. By further assumptions on the closeness and smoothness of the exact solution, a stopping rule to terminate the iteration is proposed and the suitable rates of convergence is derived.

关 键 词：非线性算子方程 非线性不适定问题 牛顿型迭代格式 迭代终止原则 收敛阶估计 

分 类 号：O241.6[理学—计算数学]