TY - JOUR T1 - A Quasi-Newton Method in Infinite-Dimensional Spaces and Its Application for Solving a Parabolic Inverse Problem AU - Yu , Wenhuan JO - Journal of Computational Mathematics VL - 4 SP - 305 EP - 318 PY - 1998 DA - 1998/08 SN - 16 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9161.html KW - Quasi-Newton method, parabolic differential equation, inverse problems in partial differential equations, linear and Q-superlinear rates of convergence. AB -

A Quasi-Newton method in Infinite-dimensional Spaces (QNIS) for solving operator 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 Fr├ęchet derivative of the governing operator is invertible. Finally, we apply QNIS to an inverse problem for a parabolic differential equation to illustrate the efficiency of the finite-dimensional algorithm.