Finite difference schemes are here solved by means of a linear matrix equation. The theoretical study of the related algebraic system is exposed, and enables us to minimize the error due to a finite difference approximation, while building a new DRP scheme in the same time. keywords DRP schemes, Sylvester equation

Canonical factorization of a rational matrix function on the unit circle is described explicitly in terms of a stabilizing solution of a discrete algebraic Riccati equation using a special state space representation of the symbol. The corresponding Riccati difference equation is also discussed. Mathematics Subject Classification (2010). Primary 47A68, 15A24; Secondary 47B35, 42A58, 39A99.

In this note we report on a new kind of algebraic Ric-cati equation which we encountered when studying an H 1 type problem of disturbance attenuation for stochastic linear systems. The same equation occurs in the analysis of stability radii of linear systems with both deterministic and stochastic uncertainties. The associated linear matrix inequality is also considered.

We construct two Osp(n|2m) solutions of the graded Yang-Baxter equation by using the algebraic braid-monoid approach. The factorizable S-matrix interpretation of these solutions is also discussed.

The main purpose of this article is to present an approximation method of for singular integrodifferential equations with Cauchy kernel in the most general form under the mixed conditions in terms of the second kind Chebyshev polynomials. This method transforms mixed singular integro-differential equations with Cauchy kernel and the given conditions into matrix equation and using the zeroes of ...

A new differential quadrature method based on quartic B-spline functions is introduced. The weighting coefficients are determined via a semi-explicit algorithm containing an algebraic equation system with four-band coefficient matrix. In order to validate the proposed method, the Burgers’ Equation is selected as test problem. The shock wave and the sinusoidal disturbance solutions of the Burger...

For the nonsymmetric algebraic Riccati equation for which the four coefficient matrices form an M -matrix, the solution of practical interest is often the minimal nonnegative solution. In this note we prove that the minimal nonnegative solution is positive when the M -matrix is irreducible.

Using an isomorphism between Hilbert spaces L and l 2 we consider Hamiltonians which have tridiagonal matrix representations (Jacobi matrices) in a discrete basis and an eigenvalue problem is reduced to solving a three term difference equation. Technique of intertwining operators is applied to creating new families of exactly solvable Jacobi matrices. It is shown that any thus obtained Jacobi m...

A new upper trace bound, which generalizes the best available similar estimates, improves their tightness and holds under a less conservative validity restriction imposed on the coefficient matrix, is derived for the solution matrix of the continuous algebraic Lyapunov equation (CALE). Two numerical examples illustrate the applicability of the main result.

We discuss how properties of Hecke symmetry (i.e., Hecke type R-matrix) influence the algebraic structure of the corresponding Reflection Equation (RE) algebra. Analogues of the Newton relations and Cayley-Hamilton theorem for the matrix of generators of the RE algebra related to a finite rank even Hecke symmetry are derived.