Matrix computations (3rd ed.)
The symmetric eigenvalue problem
The symmetric eigenvalue problem
Extended Krylov Subspaces: Approximation of the Matrix Square Root and Related Functions
SIAM Journal on Matrix Analysis and Applications
Using Generalized Cayley Transformations within an Inexact Rational Krylov Sequence Method
SIAM Journal on Matrix Analysis and Applications
Zero distributions for discrete orthogonal polynomials
Journal of Computational and Applied Mathematics
Which Eigenvalues Are Found by the Lanczos Method?
SIAM Journal on Matrix Analysis and Applications
Superlinear Convergence of Conjugate Gradients
SIAM Journal on Numerical Analysis
Convergence of the Isometric Arnoldi Process
SIAM Journal on Matrix Analysis and Applications
On the Asymptotic Spectrum of Finite Element Matrix Sequences
SIAM Journal on Numerical Analysis
An Error Analysis for Rational Galerkin Projection Applied to the Sylvester Equation
SIAM Journal on Numerical Analysis
On the ADI method for the Sylvester equation and the optimal-H2 points
Applied Numerical Mathematics
Journal of Computational and Applied Mathematics
| Hi-index | 0.00 |
Ruhe's rational Krylov method is a popular tool for approximating eigenvalues of a given matrix, though its convergence behavior is far from being fully understood. Under fairly general assumptions we characterize in an asymptotic sense which eigenvalues of a Hermitian matrix are approximated by rational Ritz values and how fast this approximation takes place. Our main tool is a constrained extremal problem from logarithmic potential theory, where an additional external field is required for taking into account the poles of the underlying rational Krylov space. Several examples illustrate our analytic results.