Laboratoire de Mathématiques Pures et Appliquées
Joseph Liouville

Séminaire Approx, EDP et Modèles aléatoires du 18 février

M. El Ghomari (Cotutelle Calais/Marrakech)

Extended Krylov subspace methods are attractive methods for computing approximations of matrix functions and other problems producing large-scale matrices. In this talk, we present the shifted extended symmetric Lanczos process for solving trace estimation problems such that trace(VTf(A)V). Here A is a large symmetric and square matrix of size n×n ; and V is a rectangular matrix of size n×s, (s<<n). This process computes approximations in the union of Krylov subspaces determined by positive powers of A and negative powers of A-σIn, where the shift σ is a user-chosen parameter. We also present how estimates of bounds for the trace can be computed by pairs of Gauss and Gauss-Radau quadrature rules, or by pairs of Gauss and anti-Gauss quadrature rules. Applications to the computation of the Estrada index for networks and to the nuclear norm of a large matrix are presented.

Informations : 13:30 - 14:30 Conférence 100% visio, BigBlueButton