波速反问题迭代算法的收敛性

Convergence of a simple computational scheme for determining the wave velocity in wave eguation

本文讨论了一维波动方程的波速反问题,将反问题归结为一个等价的非线性算子方程,利用Newton迭代法提出了一种求解非线性算子方程的简单迭代算法,应用推广的Newton-Kantorovich定理证明了迭代过程的收敛性.

This article deals with the determination of the wave velocity in 1-D wave eguation. The inverse problem is boiled down to a eguavalent nonlinear operator eguation. And a simple iterative method for the operator eguation which is based on Newton's method is presented.Usnig the generalized Newton-Kantorovich theorem, We proved the convergence of the iterative process.