Symbolic computation of Hankel determinants and matrix generalized inverses

In this thesis, existing methods for symbolic computation of Hankel deteriminants and matrix generalized inverses are modified and new are introducted. There are derived closed-form expressions for Hankel determinants of different classes of sequences. It is constructed the method for rapid computation of generalized inverses whose complexity reaches theoretical lower bound. There are also constructed new methods for computation of generalized inverses of rational and polynomial matrices

Symbolic computation of Hankel determinants and matrix generalized inverses

In this thesis, existing methods for symbolic computation of Hankel deteriminants and matrix generalized inverses are modified and new are introducted. There are derived closed-form expressions for Hankel determinants of different classes of sequences. It is constructed the method for rapid computation of generalized inverses whose complexity reaches theoretical lower bound. There are also constructed new methods for computation of generalized inverses of rational and polynomial matrices

The Hankel transform of the sum of consecutive generalized Catalan numbers

Abstract. We discuss the properties of the Hankel transformation of a sequence whose elements are the sums of consecutive generalized Catalan numbers

VISUALIZATION IN OPTIMIZATION WITH MATHEMATICA

We show how the computer algebra system in MATHEMATICA and its graphical capabilities can be used in optimization. A package for teaching the graphical solution of two-dimensional and three-dimensional linear programming problem is developed.

On the Simplex Algorithm Initializing

This paper discusses the importance of starting point in the simplex algorithm. Three different methods for finding a basic feasible solution are compared throughout performed numerical test examples. We show that our two methods on the Netlib test problems have better performances than the classical algorithm for finding initial solution. The comparison of the introduced optimization softwares is based on the number of iterative steps and on the required CPU time. It is pointed out that on average it takes more iterations to determine the starting point than the number of iterations required by the simplex algorithm to find the optimal solution