求解非线性不适定问题的隐式迭代法

基金项目: 上海市重点学科(第三期)资助项目(S30104);上海市教委重点学科建设资助项目(J50101)

Nonlinear Implicit Iterative Method for Solving Nonlinear Ill-Posed Problems

1.
Department of Mathematics, Shanghai University, Shanghai 200436, P. R. China;

摘要: 将处理线性不适定算子方程的隐式迭代法推广到非线性不适定问题，证明了迭代解误差序列的单调性，并进一步利用迭代误差的单调性得出求解非线性不适定问题隐式迭代法对精确方程和扰动方程的收敛性．
- 非线性不适定问题 /
- 非线性隐式迭代法 /
- 单调性 /
- 收敛性
Abstract: The implicit iterative method was extended for linear ill-posed operator equations to solve nonlinear ill-posed problems.It shows that under some conditions the error sequence of solutions of the nonlinear implicit iterative method is monotonically decreasing.And with this monotonicity,the convergence of the new method for both of the exact and perturbed equations was proved.
- nonlinear il-l posed problem /
- nonlinear implicit iterative method /
- monotonicity /
- convergence

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