Lehmann Bounds and Eigenvalue Error Estimation
Evgueni Ovtchinnikov · SIAM Journal on Numerical Analysis · 2011
The paper investigates the properties of Lehmann's optimal bounds for eigenvalues of Hermitian problems in order to find a way to efficiently use them for eigenvalue error estimation. A practical error estimation scheme is described that can be employed in the framework of a subspace iteration algorithm and is actually implemented by the $HSL\_ea19$ software package from the HSL Mathematical Software Library of Rutherford Appleton Laboratory.