International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 97278, 18 pages
doi:10.1155/2007/97278
Research Article
Modification of the Quasilinearization Method for the Inverse Problem
Mathematical Institute, Faculty of Applied Informatics, Tomas Bata University in Zlín, Mostní 5139, Zlín 760 01, Czech Republic
Received 25 January 2006; Revised 30 May 2006; Accepted 7 December 2006
Academic Editor: Virginia Kiryakova
Copyright © 2007 Lenka Čelechovská-Kozáková. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We propose a new modification of Bellman's quasilinearization method such that at any iteration step, it works with an approximate solution of the original nonlinear system and with new approximation of parameters α(k+1) which are close enough to the previous ones. As an output, this approach
provides a construction of a convergent sequence of parameters where the limit is
the best approximation of parameters of a given system. We apply this method to
a mathematical model describing BSP-kinetics in the human liver.