A number of basic properties about circularly-symmetric Gaussian random vectors are stated and proved here. These properties are each probably well known to most researchers who work with Gaussian noise, but I have not found them stated together with simple proofs in the literature. They are usually viewed as too advanced or too detailed for elementary texts but are used (correctly or incorrect...

The generalization of p-frame in Banach spaces is considered in this paper. The concepts of an $tilde{X}$-frame and a system conjugate to $tilde{X}$-frame were introduced. Analogues of the results on the existence of conjugate system were obtained. The stability of $tilde{X}$-frame having a conjugate system is studied.

in this paper we introduce two symmetric variants of amenability, symmetric module amenability and symmetric connes amenability. we determine symmetric module amenability and symmetric connes amenability of some concrete banach algebras. indeed, it is shown that $ell^1(s)$ is  a symmetric $ell^1(e)$-module amenable if and only if $s$ is amenable, where $s$ is an inverse semigroup with subsemigr...

This paper proposes and studies the performance of a preconditioner suitable for solving a class of symmetric positive de nite systems, Âx = b, which we call p-level lower rank extracted systems (p-level LRES), by the preconditioned conjugate gradient method. The study of these systems is motivated by the numerical approximation of integral equations with convolution kernels de ned on arbitrary...

Multi-conjugate adaptive optics (MCAO) systems with 10 − 10 degrees of freedom have been proposed for future giant telescopes. Using standard matrix methods to compute, optimize, and implement wavefront control algorithms for these systems is impractical, since the number of calculations required to compute (apply) the reconstruction matrix scales with the cube (square) of the number of AO degr...

Signal and image restoration problems are often solved by minimizing a cost function consisting of an `2 data-fidelity term and a regularization term. We consider a class of convex and edge-preserving regularization functions. In specific, half-quadratic regularization as a fixed-point iteration method is usually employed to solve this problem. The main aim of this paper is to solve the above-d...

The Seidel aberrations of a rotationally-symmetric diffractive lens with an arbitrary phase profile are presented. It is shown that by a proper choice of phase function and aperture stop position, third-order coma and astigmatism can be eliminated for any chosen conjugate ratio. Since a diffractive lens has an inherent zero value for the Petzval sum, the image plane is flat in both tangential a...

Electronic structure calculations based on Density Functional Theory (DFT) are an important branch of computational physics. We present a convergence analysis for the conjugate-gradient minimization of a Kohn-Sham energy functional, using a functional with implicit orthonormality constraints. We discuss the eeects of preconditioning, and show with a numerical example that preconditioning makes ...