Volume 16, Issue 4
A Quasi-Newton Method in Infinite-Dimensional Spaces and Its Application for Solving a Parabolic Inverse Problem

Wen-huan Yu

DOI:

J. Comp. Math., 16 (1998), pp. 305-318

Published online: 1998-08

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  • 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\'echet 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.

  • Keywords

Quasi-Newton method parabolic differential equation inverse problems in partial differential equations linear and Q-superlinear rates of convergence

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@Article{JCM-16-305, author = {}, 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\'echet 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} }
TY - JOUR T1 - A Quasi-Newton Method in Infinite-Dimensional Spaces and Its Application for Solving a Parabolic Inverse Problem 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 KW - parabolic differential equation KW - inverse problems in partial differential equations KW - 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\'echet 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.
Wen-huan Yu. (1970). A Quasi-Newton Method in Infinite-Dimensional Spaces and Its Application for Solving a Parabolic Inverse Problem. Journal of Computational Mathematics. 16 (4). 305-318. doi:
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