Produits rapides matrice-vecteur en bases d'ondelettes : application à la résolution numérique d'équations aux dérivés partielles
Projection Method for Solving a Singular System of Linear Equations and its Applications.
Proposition de préconditionneurs pseudo-différentiels pour l’équation CFIE de l’électromagnétisme
We present a weak parametrix of the operator of the CFIE equation. An interesting feature of this parametrix is that it is compatible with different discretization strategies and hence allows for the construction of efficient preconditioners dedicated to the CFIE. Furthermore, one shows that the underlying operator of the CFIE verifies an uniform discrete Inf-Sup condition which allows to predict an original convergence result of the numerical solution of the CFIE to the exact one.
Proposition de préconditionneurs pseudo-différentiels pour l'équation CFIE de l'électromagnétisme
On exhibe dans cette note une paramétrix (au sens faible) de l'opérateur sous-jacent à l'équation CFIE de l'électromagnétisme. L'intérêt de cette paramétrix est de se prêter à différentes stratégies de discrétisation et ainsi de pouvoir être utilisée comme préconditionneur de la CFIE. On montre aussi que l'opérateur sous-jacent à la CFIE satisfait une condition Inf-Sup discrète uniforme, applicable aux espaces de discrétisation usuellement rencontrés en électromagnétisme, et qui permet d'établir...
Pseudoblock conditions of diagonal dominance.
Pseudoinverse formulation of Rayleigh-Schrödinger perturbation theory for the symmetric matrix eigenvalue problem.
QMR: a quasi-minimal residual method for non-Hermitian linear systems.
QR Factorization of Toeplitz Matrices.
QR factorizations using a restricted set of rotations.
QR in two dimensions.
Quadratic convergence bounds of scaled iterates by the serial Jacobi methods for indefinite Hermitian matrices.
Quadratically constrained least squares and quadratic problems.
Quantum dynamical entropy and an algorithm by Gene Golub.
Quasi-boundary value method for non-well posed problem for a parabolic equation with integral boundary condition.
Quasi-Monte Carlo Methods for some Linear Algebra Problems. Convergence and Complexity
We present quasi-Monte Carlo analogs of Monte Carlo methods for some linear algebra problems: solving systems of linear equations, computing extreme eigenvalues, and matrix inversion. Reformulating the problems as solving integral equations with a special kernels and domains permits us to analyze the quasi-Monte Carlo methods with bounds from numerical integration. Standard Monte Carlo methods for integration provide a convergence rate of O(N^(−1/2)) using N samples. Quasi-Monte Carlo methods...
Quasi-Newton preconditioners for the inexact Newton method.
Raffinement de la borne spectrale d'un faisceau de matrices
Rank-One Modification of the Symmetric Eigenproblem.
Rational Krylov for nonlinear eigenproblems, an iterative projection method
In recent papers Ruhe suggested a rational Krylov method for nonlinear eigenproblems knitting together a secant method for linearizing the nonlinear problem and the Krylov method for the linearized problem. In this note we point out that the method can be understood as an iterative projection method. Similarly to the Arnoldi method the search space is expanded by the direction from residual inverse iteration. Numerical methods demonstrate that the rational Krylov method can be accelerated considerably...
Real and complex pseudozero sets for polynomials with applications
Pseudozeros are useful to describe how perturbations of polynomial coefficients affect its zeros. We compare two types of pseudozero sets: the complex and the real pseudozero sets. These sets differ with respect to the type of perturbations. The first set – complex perturbations of a complex polynomial – has been intensively studied while the second one – real perturbations of a real polynomial – seems to have received little attention. We present a computable formula for the real pseudozero...