This paper considers interpolating matrix polynomials P (λ) in Lagrange and Hermite bases. A classical approach to investigate the polynomial eigenvalue problem P (λ)x = 0 is linearization, by which the polynomial is converted into a larger matrix pencil with the same eigenvalues. Since the current linearizations of degree n Lagrange polynomials consist of matrix pencils with n + 2 blocks, they...

In this study‎, ‎an efficient method is presented for solving infinite boundary integro-differential equations (IBI-DE) of the second kind with degenerate kernel in terms of Laguerre polynomials‎. ‎Properties of these polynomials and operational matrix of integration are first presented‎. ‎These properties are then used to transform the integral equation to a matrix equation which corresponds t...

In this paper we prove some characterizations of the matrix orthogonal polynomials whose derivatives are also orthogonal, which generalize other known ones in the scalar case. In particular, we prove that the corresponding orthogonality matrix functional is characterized by a Pearson-type equation with two matrix polynomials of degree not greater than 2 and 1. The proofs are given for a general...

An ordering for Laurent polynomials in the algebraic torus (C∗)D, inspired by the Cantero–Moral– Velázquez approach to orthogonal Laurent polynomials in the unit circle, leads to the construction of a moment matrix for a given Borel measure in the unit torus T. The Gauss–Borel factorization of this moment matrix allows for the construction of multivariate biorthogonal Laurent polynomials in the...

Recently, a new definition for a Wigner distribution function for a one-dimensional finite quantum system, in which the position and momentum operators have a finite (multiplicityfree) spectrum, was developed. This distribution function is defined on discrete phase-space (a finite square grid), and can thus be referred to as the Wigner matrix. In the current paper, we compute this Wigner matrix...

We give a framework for formal orthogonal polynomials with respect to an arbitrary moment matrix. When the moment matrix is Hankel, this simplifies to the classical framework. The relation with Padé approximation and with Krylov subspace methods is given. 1 Formal block orthogonal polynomials We consider a linear functional defined on the space of polynomials in two variables, defined by the mo...

In this paper, we introduce the notions of weakly normal and normal matrix polynomials, with nonsingular leading coefficients. We characterize these matrix polynomials, using orthonormal systems of eigenvectors and normal eigenvalues. We also study the conditioning of the eigenvalue problem of a normal matrix polynomial, constructing an appropriate Jordan canonical form.