Reliable two-sided bounds to all eigenvalues of preconditioned matrix

  • Date:
  • Time: 14:00 - 15:30
  • Address:
    Sokolovská 83, Praha
  • Room: K3
  • Speaker: Ivana Pultarová

We consider a matrix A resulting from discretization of the weak form of an elliptic partial differential operator with variable tensor coefficient C and a preconditioning matrix $A_p$ obtained in the same way but with constant coefficient $C_p$. Any sensible boundary conditions can be applied. We present a method yielding reliable lower and upper bounds to all eigenvalues of $A_p^{-1}A$. In particular, we show how the bounds can be obtained from $C_p^{-1}C$. The discretization techniques such as finite element method, finite difference method, or stochastic Galerkin methods can be used.