A quasi-Newton method in infinite-dimensional spaces and its application for solving a parabolic inverse problem

摘要

A Quasi-Newton method in Infinite-dimensional Spaces(QNIS) for solving op- erator equations is presented and the convergence of a sequence generated by QNIS is also proved in the paper. Next, we suggest a finite-dimensional implementation of QNIS and prove that the sequence defined by the finite-dimensional algorithm converges to the root of the original operator equation providing that the later exists and that the Frechet derivative of the governing operator is invertible. Fi- nally, we apply QNIS to an inverse problem for a parabolic differential equation to illustrate the efficiency of the finite-dimensional algorithm.