In recent years, there has been greater attempt to find numerical solutions of differential equations using wavelet's methods. The following method is based on vector forms of Haar-wavelet functions. In this paper, we will introduce one dimensional Haar-wavelet functions and the Haar-wavelet operational matrices of the fractional order integration. Also the Haar-wavelet operational matrices of ...

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...

Abstract. We present new formulae for the “near” inverses of striped Sylvester and mosaic Sylvester matrices. The formulae assume computation over floating-point rather than exact arithmetic domains. The near inverses are expressed in terms of numerical Padé-Hermite systems and simultaneous Padé systems. These systems are approximants for the power series determined from the coefficients of the...

We consider inverse boundary value problems in Rn, n ≥ 3, for operators which may be written as first order perturbations of the Laplacian. The purpose is to obtain global uniqueness theorems for such problems when the coefficients are nonsmooth. We use complex geometrical optics solutions of Sylvester-Uhlmann type to achieve this. A main tool is an extension of the Nakamura-Uhlmann intertwinin...

General parametric solution to a family of generalized Sylvester matrix equations arising in linear system theory is presented by using the socalled generalized Sylvester mapping which has some elegant properties. The solution consists of some polynomial matrices satisfying certain conditions and a parametric matrix representing the degree of freedom in the solution. The results provide great c...

A new numerical procedure is proposed to solve the symmetric matrix polynomial equation A T (?s)X(s) + X T (?s)A(s) = 2B(s) that is frequently encountered in control and signal processing. It is based on interpolation and takes fully advantage of symmetry of the equation by reducing the original problem dimension. The algorithm is more eecient and more general than older methods and, namely, it...

This paper is concerned with numerical solutions to general linear matrix equations including the wellknown Lyapunov matrix equation and Sylvester matrix equation as special cases. Gradient based iterative algorithm is proposed to approximate the exact solution. A necessary and sufficient condition guaranteeing the convergence of the algorithm is presented. A sufficient condition that is easy t...