Comparison of an improved self-consistent lower bound theory with Lehmann's method for low-lying eigenvalues.

ABSTRACT: Ritz eigenvalues only provide upper bounds for the energy levels, while obtaining lower bounds requires at least the calculation of the variances associated with these eigenvalues. The well-known Weinstein and Temple lower bounds based on the eigenvalues and variances converge very slowly and their quality is considerably worse than that of the Ritz upper bounds. Lehmann presented a method that in principle optimizes Temple's lower bounds with significantly improved results. We have recently formulated a Self-Consistent Lower Bound Theory (SCLBT), which improves upon Temple's results. In this paper, we further improve the SCLBT and compare its quality with Lehmann's theory. The Lánczos algorithm for constructing the Hamiltonian matrix simplifies Lehmann's theory and is essential for the SC

SUBMITTER: Ronto M 

PROVIDER: S-EPMC8648772 | biostudies-literature | 2021 Dec

REPOSITORIES: biostudies-literature