The new generalized Harry Dym equation of Z. Popowicz is transformed into the Hirota–Satsuma system of coupled KdV equations.

In this work, we investigate the interval generalized Sylvester matrix equation AXB+ CXD = F and develop some techniques for obtaining outer estimations for the so-called united solution set of this interval system. First, we propose a modified variant of the Krawczyk operator which causes reducing computational complexity to cubic, compared to Kronecker product form. We then propose an iterati...

In this paper, an iterative method is constructed to find the least-squares solutions of generalized Sylvester equation A X B A X B A X B A X B C 1 1 1 2 2 2 3 3 3 4 4 4 + + + = , where [ ] X X X X 1 2 3 4 , , , is real matrices group, and i X satisfies different linear constraint. By this iterative method, for any initial matrix group ( ) ( ) ( ) ( )     X X X X 0 0 0 0 1 2 3 4 , , , withi...

The delay Lyapunov equation is an important matrix boundary-value problem which arises as an analogue of the Lyapunov equation in the study of time-delay systems ẋ(t) = A0x(t) +A1x(t− τ) +B0u(t). We propose a new algorithm for the solution of the delay Lyapunov equation. Our method is based on the fact that the delay Lyapunov equation can be expressed as a linear system of equations, whose unkn...

The new generalized Harry Dym equation of Z. Popowicz is transformed into the Hirota–Satsuma system of coupled KdV equations.

We provide a formula for variational quasi-Newton updates with multiple weighted secant equations. The derivation of the formula leads to a Sylvester equation in the correction matrix. Examples are given.

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