Raffinement de la borne spectrale d'un faisceau de matrices
Regular Splittings and the Discrete Neumann Problem.
Reguläre Zerlegungen und Berechnung des Spektralradius nichtnegativer Matrizen.
Regularization and stabilization of discrete saddle-point variational problems.
Relations Between Condition Numbers and the Convergence of the Jacobi Method for Real Positive Definite Matrices.
Relaxation bei komplexen Matrizen.
Relaxation bei nichtsymmetrischen Matrizen.
Remarks on polynomial methods for solving systems of linear algebraic equations
For a large system of linear algebraic equations , the approximate solution is computed as the -th order Fourier development of the function , related to orthogonal polynomials in space. The domain in the complex plane is assumed to be known. This domain contains the spectrum of the matrix . Two algorithms for are discussed. Two possibilities of preconditioning by an application of the so called Richardson iteration process with a constant relaxation coefficient are proposed. The case...
Remarques sur la convergence de la méthode Q.R.
Remarques sur les algorithmes de décomposition de domaines
Resilient asynchronous primal Schur method
This paper introduces the application of asynchronous iterations theory within the framework of the primal Schur domain decomposition method. A suitable relaxation scheme is designed, whose asynchronous convergence is established under classical spectral radius conditions. For the usual case where local Schur complement matrices are not constructed, suitable splittings based only on explicitly generated matrices are provided. Numerical experiments are conducted on a supercomputer for both Poisson's...
Résolution de grands systèmes linéaires creux par méthodes itératives parallèles
Résolution paramétrée de familles de systèmes linéaires
Retooling the method of block conjugate gradients.
Robust domain decomposition preconditioners for abstract symmetric positive definite bilinear forms
An abstract framework for constructing stable decompositions of the spaces corresponding to general symmetric positive definite problems into “local” subspaces and a global “coarse” space is developed. Particular applications of this abstract framework include practically important problems in porous media applications such as: the scalar elliptic (pressure) equation and the stream function formulation of its mixed form, Stokes’ and Brinkman’s equations. The constant in the corresponding abstract...
Robust domain decomposition preconditioners for abstract symmetric positive definite bilinear forms
An abstract framework for constructing stable decompositions of the spaces corresponding to general symmetric positive definite problems into “local” subspaces and a global “coarse” space is developed. Particular applications of this abstract framework include practically important problems in porous media applications such as: the scalar elliptic (pressure) equation and the stream function formulation of its mixed form, Stokes’ and Brinkman’s equations....
Robustness of multi-grid applied to anisotropic equations on convex domains with re-entrant corners.
Round-Off Error Analysis of Iterations for Large Linear Systems.
Round-off error analysis of the gradient method