A Refinement of some Overrelaxation Algorithms for Solving a System of Linear Equations

In this paper we propose a refinement of some successive overrelaxation methods based on the reverse Gauss–Seidel method for solving a system of linear equations Ax = b by the decomposition A = Tm − Em − Fm, where Tm is a banded matrix of bandwidth 2m + 1. We study the convergence of the methods and give software implementation of algorithms in Mathematica package with numerical examples. ACM Computing Classification System (1998): G.1.3.

Parameter Identification of a Fed-Batch Cultivation of S. Cerevisiae using Genetic Algorithms

Fermentation processes as objects of modelling and high-quality control are characterized with interdependence and time-varying of process variables that lead to non-linear models with a very complex structure. This is why the conventional optimization methods cannot lead to a satisfied solution. As an alternative, genetic algorithms, like the stochastic global optimization method, can be applied to overcome these limitations. The application of genetic algorithms is a precondition for robustness and reaching of a global minimum that makes them eligible and more workable for parameter identification of fermentation models. Different types of genetic algorithms, namely simple, modified and multi-population ones, have been applied and compared for estimation of nonlinear dynamic model parameters of fed-batch cultivation of S. cerevisiae.

A Linear Time Algorithm for Computing Longest Paths in Cactus Graphs

ACM Computing Classification System (1998): G.2.2.

Optimization Problem in a Class of Linear System. Application to Multiple Drug Administration

2000 Mathematics Subject Classification: 62H15, 62P10.

Linear Colligations and Dynamic System Corresponding to Operators in the Banach Space

2000 Mathematics Subject Classification: Primary 47A48, 93B28, 47A65; Secondary 34C94.