In this paper properties of cell matrices are studied. A determinant of such a matrix is given in a closed form. In the proof a general method for determining a determinant of a symbolic matrix with polynomial entries, based on multivariate polynomial Lagrange interpolation, is outlined. It is shown that a cell matrix of size n > 1 has exactly one positive eigenvalue. Using this result it is pr...

In this paper, a new collocation method, which is based on Boubaker polynomials, is introduced for the approximate solutions of a class of two-dimensional linear Fredholm integral equationsof the second kind. The properties of two-dimensional Boubaker functions are presented. The fundamental matrices of integration with the collocation points are utilized to reduce the solution of the integral ...

The Extended Euclidean algorithm for matrix Pade approximants is applied to compute matrix Pade approximants in rectangular full packed format (RFP) if the coefficient matrices of the input matrix polynomial are triangular. The procedure given by Gustavson et al for packing a triangular matrix in rectangular full packed format is applied to pack sequence of lower triangular matrices of a matrix...

In this paper, we will show that the width of simplices defined by systems of linear inequalities can be computed in polynomial time if some minors of their constraint matrices are bounded. Additionally, we present some quasi-polynomial-time and polynomial-time algorithms to solve the integer linear optimization problem defined on simplices minus all their integer vertices assuming that some mi...