The Rayleigh–Ritz Technique for Estimating Eigenvalues

The energy principle provides a powerful technique for determining the stability or instability of a magneto-fluid system without resorting to the solution of a differential equation. Instead, one makes an educated guess at the minimizing displacement and then examines the sign of the resulting eigenvalue. This approach is made even more powerful, and put on a solid theoretical footing, by application of the Rayleigh–Ritz technique for estimating the eigenvalues of a self-adjoint operator.

It is the mark of an educated mind to rest satisfied with the degree of precision which the nature of the subject admits and not to seek exactness where only an approximation is possible.

Aristotle