Three methods for two-sided bounds of eigenvalues - a comparison
For researchers in numerical analysis, this is an incremental comparison of existing methods for eigenvalue bounds.
The paper compares three finite element methods for computing two-sided bounds of eigenvalues of symmetric elliptic operators, evaluating their accuracy, computational performance, and generality through numerical examples.
We compare three finite element based methods designed for two-sided bounds of eigenvalues of symmetric elliptic second order operators. The first method is known as the Lehmann-Goerisch method. The second method is based on Crouzeix-Raviart nonconforming finite element method. The third one is a combination of generalized Weinstein and Kato bounds with complementarity based estimators. We concisely describe these methods and use them to solve three numerical examples. We compare their accuracy, computational performance, and generality in both the lowest and higher order case.