An extension of the rayleigh-ritz method for finding upper and lower bounds of eigenvalues
R. A. Sack · International Journal of Quantum Chemistry · 2009
A simple variational method is described for the determination of upper and lower bounds for the eigenvalues of an Hermitian operator M. For a selected vector subspace of n dimensions it involves the diagonalization of a 2n × 2n matrix, the elements of which depend on the matrix elements of M and M 2 as well as on upper and lower bounds of M in the complementary subspace. The method is equivalent to one given by H. F. Weinberger; it includes the Rayleigh-Ritz procedure and a modified form of Temple's formula as limiting cases.