The current paper proposes a technique for the numerical solution of linear control systems.The method is based on Galerkin method, which uses the interpolating scaling functions. For a highly accurate connection between functions and their derivatives, an operational matrix for the derivatives is established to reduce the problem to a set of algebraic equations. Several test problems are given...

This paper presents an approach for solving a nonlinear stochastic differential equations (NSDEs) using a new basis functions (NBFs). These functions and their operational matrices are used for representing matrix form of the NBFs. With using this method in combination with the collocation method, the NSDEs are reduced a stochastic nonlinear system of equations and unknowns. Then, the error ana...

In the present paper, a numerical method is considered for solving one-dimensional heat equation subject to both Neumann and Dirichlet initial boundary conditions. This method is a combination of collocation method and radial basis functions (RBFs). The operational matrix of derivative for Laguerre-Gaussians (LG) radial basis functions is used to reduce the problem to a set of algebraic equatio...

In the present work, under some di¤erentiability conditions on the potential functions , we …rst reduce the inverse scattering problem (ISP) for the polynomial pencil of the Scroedinger equation to the corresponding ISP for the generalized matrix Scrödinger equation . Then ISP will be solved in analogy of the Marchenko method. We aim to establish an e¤ective algorithm for uniquely reconstructin...

The Discrete Logarithm and the Diffie-Hellman are two hard computational problems, closely related to cryptography and its applications. The computational equivalence of these problems has been proved only for some special cases. In this study, using LU-decomposition to Vandermonde matrices, we are able to transform the two problems in terms of matrices, thus giving a new perspective to their e...

We study in this paper very badly approximable matrix functions on the unit circle T, i.e., matrix functions Φ such that the zero function is a superoptimal approximation of Φ. The purpose of this paper is to obtain a characterization of the continuous very badly approximable functions. Our characterization is more geometric than algebraic characterizations earlier obtained in [PY1] and [AP]. I...

Matrix functions preserving several sets of generalized nonnegative matrices are characterized. These sets include PFn, the set of n×n real eventually positive matrices; and WPFn, the set of matrices A ∈ R such that A and its transpose have the Perron-Frobenius property. Necessary conditions and sufficient conditions for a matrix function to preserve the set of n× n real eventually nonnegative ...

We investigate existing and novel methods to approximate matrix functions using subspace methods. We analyze a two-sided harmonic Ritz approach and apply this to the extraction from a subspace for matrix functions. We derive all methods in various ways and provide a framework to fit in the techniques.

The mathematic of belief functions can be handled by the use of the matrix notation. This representation helps greatly the user thanks to its notational simplicity and its efficiency for proving theorems. We show how to use them for several problems related to belief functions and the transferable belief model.