Some algorithms for nding common xed point of a family of mappings isconstructed. Indeed, let C be a nonempty closed convex subset of a uniformlyconvex Banach space X whose norm is Gateaux dierentiable and let {Tn} bea family of self-mappings on C such that the set of all common fixed pointsof {Tn} is nonempty. We construct a sequence {xn} generated by the hybridmethod and also we give the cond...

The theory of c-frames and c-Bessel mappings are the generalizationsof the theory of frames and Bessel sequences. In this paper, weobtain several equivalent conditions for dual of c-Bessel mappings.We show that for a c-Bessel mapping $f$, a retrievalformula with respect to a c-Bessel mapping $g$ is satisfied if andonly if $g$ is sum of the canonical dual of $f$ with a c-Besselmapping which  wea...

In this article, we consider the matrix equation $AXB=C$, where A, B, C are given matrices and give new necessary and sufficient conditions for the existence of the diagonal solutions and monomial solutions to this equation. We also present a general form of such solutions. Moreover, we consider the least squares problem $min_X |C-AXB |_F$ where $X$ is a diagonal or monomial matrix. The explici...

It is widely known that the solutions of Lyapunov equations can be used to compute the H2 norm of linear timeinvariant (LTI) dynamical systems. In this paper, we show how this theory extends to dynamical systems with delays. The first result is that the H2 norm can be computed from the solution of a generalization of the Lyapunov equation, which is known as the delay Lyapunov equation. From the...

It is widely known that the solutions of Lyapunov equations can be used to compute the H2 norm of linear timeinvariant (LTI) dynamical systems. In this paper, we show how this theory extends to dynamical systems with delays. The first result is that the H2 norm can be computed from the solution of a generalization of the Lyapunov equation, which is known as the delay Lyapunov equation. From the...

in this paper we study the properties of derivations of a b, where a and b are simple separable c*-algebras, and a b is the c*-completion of a b with respect to a c*-norm yon a b and we will characterize the derivations of a b in terms of the derivations of a and b

We consider a class of matrix spectral norm approximation problems for finding an affine combination of given matrices having the minimal spectral norm subject to some prescribed linear equality and inequality constraints. These problems arise often in numerical algebra, engineering and other areas, such as finding Chebyshev polynomials of matrices and fastest mixing Markov chain models. Based ...

The näıve Nyström extension forms a low-rank approximation to a positive-semidefinite matrix by uniformly randomly sampling from its columns. This paper provides the first relativeerror bound on the spectral norm error incurred in this process. This bound follows from a natural connection between the Nyström extension and the column subset selection problem. The main tool is a matrix Chernoff b...

Current research proposes a natural environment for the space-time codes and in this context it is obtained a new design criterion for space-time codes in multi-antenna communication channels. The objective of this criterion is to minimize the pairwise error probability of the maximum likelihood decoder, endowed with the matrix spectrum norm. The random matrix theory is used and an approximatio...

A speech enhancement method employing sparse reconstruction of the power spectral density is proposed. The overcomplete dictionary of the power spectral density is learned by approximation K-singular value decomposition algorithm with non negative constraint. The power spectral density of clean speech signal is reconstructed by least angle regression method with a norm termination rule, and the...