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

Lenka Čelechovská-Kozáková

 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

Recommended by Virginia Kiryakova

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.