Rayleigh–Ritz method

Summary

The Rayleigh–Ritz method approximates the eigenvalues of a self-adjoint operator by restricting its Rayleigh quotient to a finite-dimensional space of trial vectors. This reduces the problem to a small matrix eigenvalue problem. By the min-max theorem, each approximate eigenvalue is an upper bound for the corresponding true one, and the bounds improve as the trial space grows. The method underlies the finite element computation of vibration modes and many iterative eigenvalue solvers.