Über die numerische Berechnung der Eigenwerte von Säkulargleichungen

Summary

The calculation of the eigenvalues of secular-equations is a difficult and tedious task. Even with a five-ordered determinant it is very time-consuming to evaluate the minors in the usual way. The purpose of this paper is to describe a simple method to transform the secular determinant into its algebraic form. By consequent combination of rows of the determinant all elements which are standing under the main-diagonal are eliminated, so that the value of the determinant is represented only by the product of the diagonal elements. This method can be used with the normal calculating-machine. The tabular scheme of the calculation also makes it possible for a quick execution of secular-equations of higher degrees.