@Article{JCM-16-305, author = {Yu , Wenhuan}, title = {A Quasi-Newton Method in Infinite-Dimensional Spaces and Its Application for Solving a Parabolic Inverse Problem}, journal = {Journal of Computational Mathematics}, year = {1998}, volume = {16}, number = {4}, pages = {305--318}, abstract = {

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. 

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9161.html} }