In this paper, a uniformly elliptic second order boundary value problem in 2D is discretized by the p-version of the finite element method. An inexact Dirichlet-Dirichlet domain decomposition pre-conditioner for the system of linear algebraic equations is investigated. The ingredients of such a pre-conditioner are an pre-conditioner for the Schur complement, an preconditioner for the sub-domain...

This paper presents a proximal point approach for computing the Riemannian or intrinsic Karcher mean of, n×n, symmetric positive definite (SPD) matrices. Our method derives from proximal point algorithm with Schur decomposition developed to compute minimum points of convex functions on SPD matrices set when it is seen as a Hadamard manifold. The main idea of the original method is preserved. Ho...

In this paper, a uniformly elliptic second order boundary value problem in 2D is discretized by the p-version of the finite element method. An inexact Dirichlet-Dirichlet domain decomposition pre-conditioner for the system of linear algebraic equations is investigated. The ingredients of such a pre-conditioner are an pre-conditioner for the Schur complement, an preconditioner for the sub-domain...

Watermarking is a technique which consists in introducing a brand, the name or the logo of the author, in an image in order to protect it against illegal copy. The capacity of the existing watermark channel is often limited. We propose in this paper a new robust method which consists in adding the triangular matrix of the mark obtained after the Schur decomposition to the DCT transform of the h...

A new class of high-performance preconditioned iterative solution methods for large-scale finite element method (FEM) elliptic systems is proposed and analyzed. The non-overlapping domain decomposition (DD) naturally introduces coupling operator at the interface γ. In general, γ a manifold lower dimensions. At level, key property that energy norm associated with Steklov-Poincaré spectrally equi...

Spectral clustering methods are based on solving eigenvalue problems for the identification of clusters, e.g., the identification of metastable subsets of a Markov chain. Usually, real-valued eigenvectors are mandatory for this type of algorithms. The Perron Cluster Analysis (PCCA+) is a well-known spectral clustering method of Markov chains. It is applicable for reversible Markov chains, becau...

This paper considers the synthesis of non-fragile H∞ state feedback controllers for singular systems and static state feedback controller with multiplicative uncertainty. The sufficient condition of controller existence, the design method of non-fragile H∞ controller, and the measure of non-fragility in controller are presented via LMI(linear matrix inequality) technique. Also, through singular...

Abstract. The modeling of the microphysics of a population of atmospheric particles interacting through a common medium leads to the solution of a large system of weakly coupled differential-algebraic equations. An implicit time discretization of the system of differential-algebraic equations is solved with a Newton method at each time step. The structure of the global system and the sparsity o...

In this article we introduce the category of noncommutative Artin motives as well as the category of noncommutative mixed Artin motives. In the pure world, we start by proving that the classical category AM(k)Q of Artin motives (over a base field k) can be characterized as the largest category inside Chow motives which fully-embeds into noncommutative Chow motives. Making use of a refined bridg...