Palindromic polynomial eigenvalue problems and related classes of structured eigenvalue problems are considered. These structures generalize the concepts of symplectic and Hamiltonian matrices to matrix polynomials. We discuss several applications where these matrix polynomials arise, and show how linearizations can be derived that reflect the structure of all these structured matrix polynomial...

Weak-star asymptotic results are obtained for the zeros of orthogonal matrix polynomials (i.e. the zeros of their determinants) on R from two di®erent assumptions: ̄rst from the convergence of matrix coe±cients occurring in the three-term recurrence for these polynomials and, second, from some conditions on the generating matrix measure. The matrix analogue of the Chebyshev polynomials of the ̄...

In this ‎article‎‎, ‎an ‎ap‎plied matrix method, which is based on Bernouli Polynomials, has been presented to find approximate solutions of ‎high order ‎Volterra ‎integro-differential‎ equations. Through utilizing this approach, the proposed equations reduce to a system of algebric equations with unknown Bernouli coefficients. A number of numerical ‎illustrations‎ have been ‎solved‎ to ‎assert...

In the last two years Frobenius-Euler polynomials have gained renewed interest and were studied by several authors. This paper presents a novel approach to these polynomials by treating them as Appell polynomials. This allows to apply an elementary matrix representation based on a nilpotent creation matrix for proving some of the main properties of Frobenius-Euler polynomials in a straightforwa...

In this paper we derive a fast O(n) algorithm for solving linear systems where the coefficient matrix is a polynomial-Vandermonde VR(x) = [rj−1(xi)] matrix with polynomials R related to a quasiseparable matrix. The result is a generalization of the well-known Björck-Pereyra algorithm for classical Vandermonde systems. As will be shown, many important systems of polynomials are related to quasis...

First, we derive explicit computable expressions of structured backward errors of approximate eigenelements of structured matrix polynomials including symmetric, skew-symmetric, Hermitian, skew-Hermitian, even and odd polynomials. We also determine minimal structured perturbations for which approximate eigenelements are exact eigenelements of the perturbed polynomials. Next, we analyze the effe...

where U, V are scalar functions defined on R. The model was termed the Cauchy matrix model because of the shape of the coupling term. Similarly to the case of the Hermitean one-matrix models for which the spectral statistics is expressible in terms of appropriate orthogonal polynomials [3], this two-matrix model is solvable with the help of a new family of biorthogonal polynomials named the Cau...

For little q-Jacobi polynomials, q-Hahn polynomials and big q-Jacobi polynomials we give particular q-hypergeometric series representations in which the termwise q = 0 limit can be taken. When rewritten in matrix form, these series representations can be viewed as decompositions into a lower triangular matrix times upper triangular matrix. We develop a general theory of such decompositions rela...