In this paper, we develop a multidimensional companding scheme for the preceptual distortion measure by S. van de Par [1]. The scheme is asymptotically optimal in the sense that it has a vanishing rate-loss with increasing vector dimension. The compressor operates in the frequency domain: in its simplest form, it pointwise multiplies the Discrete Fourier Transform (DFT) of the windowed input si...

In this paper we present an iterative method, inspired by the inverse iteration with shift technique of finite linear algebra, designed to find the eigenvalues and eigenfunctions of the Laplacian with homogeneous Dirichlet boundary condition for arbitrary bounded domains X R . This method, which has a direct functional analysis approach, does not approximate the eigenvalues of the Laplacian as ...

In this paper we discuss an abstract iteration scheme for the calculation of the smallest eigenvalue of an elliptic operator eigenvalue problem. A short and geometric proof based on the preconditioned inverse iteration (PINVIT) for matrices [Knyazev and Neymeyr, (2009)] is extended to the case of operators. We show that convergence is retained up to any tolerance if one only uses approximate ap...

We examine the problem of maximum likelihood covariance estimation using a sensor array in which the relative positions of individual sensors change over the observation interval The problem is cast as one of estimating a structured covariance matrix sequence. A vector space structure is imposed on such sequences, and within that vector space we define a constraint space given by the intersecti...

In this paper, we prove a strong convergence theorem of modified Ishikawa iteration processes by the new hybrid iterative method introduced by Takahashi et al. (2008) for two relatively asymptotically nonexpansive mappings in Banach spaces under some appropriate conditions. Furthermore, our result improves and generalizes the corresponding results announced by many others. The project was suppo...

In this paper, we will use a modified  variational iteration method (MVIM) for solving an inverse heat conduction problem (IHCP). The approximation of the temperature and the heat flux at  are considered. This method is based on the use of Lagrange multipliers for the identification of optimal values of parameters in a functional in Euclidian space. Applying this technique, a rapid convergent s...

In this paper, an iterative method is proposed for solving the matrix inverse problem $AX=B$ for Hermitian-generalized Hamiltonian matrices with a submatrix constraint. By this iterative method, for any initial matrix $A_0$, a solution $A^*$ can be obtained in finite iteration steps in the absence of roundoff errors, and the solution with least norm can be obtained by choosing a special kind of...

Time-delays are important components of many dynamical systems that describe coupling or interconnection between dynamics, propagation or transport phenomena, and heredity and competition in population dynamics. The stabilization with time delay in observation or control represents difficult mathematical challenges in the control of distributed parameter systems. It is well-known that the stabi...