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...

This paper presents a menu-driven RATS-program which allows to identify structural shocks in vector-autoregressive (VAR) models. Identification is achieved by imposing short-run or long-run restrictions (or a combination of both) on the structural form of a model. The only requirement is that the matrix of restrictions consisting of rows of the restricted matrices of short-run and long-run effe...

This paper deals with modeling and parameter identification of nonlinear systems described by Hammerstein model having Piecewise nonlinear characteristics such as Dead-zone nonlinearity characteristic. The simultaneous use of both an easy decomposition technique and the triangular basis functions leads to a particular form of Hammerstein model. The approximation by using Triangular basis functi...

This paper proposes an efficient algorithm for simultaneous reduction of three matrices. The algorithm is a blocked version of the algorithm described by Miminis and Page (1982) which reduces A to the m-Hessenberg form, and B and E to the triangular form. The m-Hessenberg– triangular–triangular form of matrices A, B and E is specially suitable for solving multiple shifted systems. Such shifted ...

In the paper triangular graphs are discussed. The class of triangular graphs is of special interest as unifying basic features of complete graphs with trees and being used on many various occasions. They model processor networks in which local computations can be easily implemented. The main issue addressed in the paper is to characterize class of triangular graphs (defined globally) by local m...