The relative error in the Pruess method for Sturm-Liouville problems (Q1976922)

The author commences by stating with references, a number of theorems connected with the eigenvalues of one-dimensional Sturm-Liouville equations. He then explains the Pruess method of approximating the eigenvalues and proves some theorems connected with the errors arising in its use. It is shown that, in one particular case, the error is very small. A curious feature is that the dependence of the considered error is almost constant for eigenvalues greater than the tenth.