Normal matrix polynomials with nonsingular leading coefficients.
On a criterion of D-stability for P-matrices
In this paper, we study positive stability and D-stability of P-matrices.We introduce the property of Dθ-stability, i.e., the stability with respect to a given order θ. For an n × n P-matrix A, we prove a new criterion of D-stability and Dθ-stability, based on the properties of matrix scalings.
On Condition Numbers and the Distance to the Nearest Ill-posed Problem.
On condition numbers of a nondefective multiple eigenvalue.
On perfect conditioning of Vandermonde matrices on the unit circle.
On the Frobenius condition number of positive definite matrices.
One-sided simultaneous inequalities and sandwich theorems for diagonal similarity and diagonal equivalence of nonnegative matrices.
Optimally Conditioned Vandermonde Matrices.
Probability against condition number and sampling of multivariate trigonometric random polynomials.
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...
Solution of the problem of optimal diagonal scaling for quasi-real Hermitian positive-definite matrices.
Some new results on determinantal inequalities and applications.
Stabilité numérique de l'algorithme de Levinson
Stable vector bundles over cuspidal cubics
We give a complete classification of stable vector bundles over a cuspidal cubic and calculate their cohomologies. The technique of matrix problems is used, similar to [2, 3].
Structured condition numbers and backward errors in scalar product spaces.
Structured conditioning of matrix functions.
Structured low rank approximations of the sylvester resultant matrix for approximate GCDS of Bernstein basis polynomials.
The norm of the product of a large matrix and a random vector.
The structured sensitivity of Vandermonde-like systems.