Etudes sur les e- et g-algorithmes.
Explicit expressions for the coordinates of foci and vertices of a quadric in dependence on the coefficients of its Cartesian equations
Improving the convergence of iterative methods
The author considers the operator equation . Methods for acceleration of convergence of the iterative process are investigated.
Multilevel correction adaptive finite element method for semilinear elliptic equation
A type of adaptive finite element method is presented for semilinear elliptic problems based on multilevel correction scheme. The main idea of the method is to transform the semilinear elliptic equation into a sequence of linearized boundary value problems on the adaptive partitions and some semilinear elliptic problems on very low dimensional finite element spaces. Hence, solving the semilinear elliptic problem can reach almost the same efficiency as the adaptive method for the associated boundary...
Non-monotoneous parallel iteration for solving convex feasibility problems
The method of projections onto convex sets to find a point in the intersection of a finite number of closed convex sets in an Euclidean space, sometimes leads to slow convergence of the constructed sequence. Such slow convergence depends both on the choice of the starting point and on the monotoneous behaviour of the usual algorithms. As there is normally no indication of how to choose the starting point in order to avoid slow convergence, we present in this paper a non-monotoneous parallel algorithm...
Nouvelles formulations intégrales pour les problèmes de diffraction d’ondes
We present an integral equation method for solving boundary value problems of the Helmholtz equation in unbounded domains. The method relies on the factorisation of one of the Calderón projectors by an operator approximating the exterior admittance (Dirichlet to Neumann) operator of the scattering obstacle. We show how the pseudo-differential calculus allows us to construct such approximations and that this yields integral equations without internal resonances and being well-conditioned at all frequencies....
Nouvelles formulations intégrales pour les problèmes de diffraction d'ondes
We present an integral equation method for solving boundary value problems of the Helmholtz equation in unbounded domains. The method relies on the factorisation of one of the Calderón projectors by an operator approximating the exterior admittance (Dirichlet to Neumann) operator of the scattering obstacle. We show how the pseudo-differential calculus allows us to construct such approximations and that this yields integral equations without internal resonances and being well-conditioned at all...
On the Numerical Evaluation of a Sum Involving Binomial Coefficients.
On the parameter selection problem in the Newton-ADI iteration for large-scale Riccati equations.
Particular Rules for the Vector e-Algorithm.
Periodic analogues of the Euler-Maclaurin and Poisson summation formulas with applications to number theory
Postprocessing and higher order convergence for the mixed finite element approximations of the Stokes eigenvalue problems
In this paper we propose a method for improving the convergence rate of the mixed finite element approximations for the Stokes eigenvalue problem. It is based on a postprocessing strategy that consists of solving an additional Stokes source problem on an augmented mixed finite element space which can be constructed either by refining the mesh or by using the same mesh but increasing the order of the mixed finite element space.
Réduction de la résolution d'un problème de réseau maillé (B) : sur la convergence locale de certaines méthodes
Sequence transformations and linear recurrences of higher order
Series approximations to powers of
Superconvergence of a stabilized approximation for the Stokes eigenvalue problem by projection method
This paper presents a superconvergence result based on projection method for stabilized finite element approximation of the Stokes eigenvalue problem. The projection method is a postprocessing procedure that constructs a new approximation by using the least squares method. The paper complements the work of Li et al. (2012), which establishes the superconvergence result of the Stokes equations by the stabilized finite element method. Moreover, numerical tests confirm the theoretical analysis.
Применение нормализованного разложения к решению частичной проблемы собственных значений матрицы