Rayleigh Quotient Iteration - Algorithm

Algorithm

The algorithm is very similar to inverse iteration, but replaces the estimated eigenvalue at the end of each iteration with the Rayleigh quotient. Begin by choosing some value as an initial eigenvalue guess for the Hermitian matrix . An initial vector must also be supplied as initial eigenvector guess.

Calculate the next approximation of the eigenvector by

where is the identity matrix, and set the next approximation of the eigenvalue to the Rayleigh quotient of the current iteration equal to

To compute more than one eigenvalue, the algorithm can be combined with a deflation technique.