This article introduces a new application of piecewise linear orthogonal triangular functions to solve fractional order differential-algebraic equations. The generalized triangular function operational matrices for approximating Riemann-Liouville fractional order integral in the triangular function (TF) domain are derived. Error analysis is carried out to estimate the upper bound of absolute er...

We introduce a generalization of the Parikh mapping called the Parikh q-matrix encoding, which takes its values in matrices with polynomial entries. The encoding represents a word w over a k-letter alphabet as a (k + 1)-dimensional upper-triangular matrix with entries that are nonnegative integral polynomials in variable q. Putting q = 1, we obtain the morphism introduced by Mateescu, Salomaa, ...

Abstract. Let B+ ⊂ GLn(R) denote the subgroup of upper triangular n × nmatrices with positive entries on the main diagonal. A matrix M ∈ B+ is called totally positive if the determinants of all its minors not containing a row or column lying completely under the main diagonal are positive. We give a simple determinantal equation for the boundary of all positive upper triangular matrices in B+.

We give a review of the theory of factorization of block Toeplitz matrices of the type T = (Ti−j)i,j∈Zd , where Ti−j are complex k × k matrices, in the form T = LDU, with L and L−1 lower block triangular, U and U−1 upper block triangular Toeplitz matrices, and D a diagonal matrix function. In particular, it is discussed how decay properties of Ti a ect decay properties of L, L−1, U , and U−1. W...

The purpose of this article is to study determinants of matrices which are known as generalized Pascal triangles (see [1]). We present a factorization by expressing such a matrix as a product of a unipotent lower triangular matrix, a Töeplitz matrix and a unipotent upper triangular matrix. The determinant of a generalized Pascal matrix equals thus the determinant of a Töeplitz matrix. This equa...

Abstract. In this paper we will present a general framework for solving linear systems of equations. The solver is based on the Levinson-idea for solving Toeplitz systems of equations. We will consider a general class of matrices, defined as the class of simple -Levinson conform matrices. This class incorporates, for instance, semiseparable, band, companion, arrowhead and many other matrices. F...