On the relative accuracies of eigenvalue bounds

The authors examine the relative accuracies of the Rayleigh upper bound and the Temple (1928), Weinstein (1934) and Stevenson (1938) lower bounds in the limit of an accurate trial function. This analysis leads to an understanding of why lower bounds have usually been observed to have larger errors than upper bounds using the same trial function. In the second part a simple relationship is given between the errors in classical lower bounds, and intermediate- operator lower bounds. The relative errors of Rayleigh and intermediate-operator methods are examined in the limit of an accurate trial function.