Editing Rayleigh quotient iteration (section)

'''Rayleigh quotient iteration''' is an [[eigenvalue algorithm]] which extends the idea of the [[inverse iteration]] by using the [[Rayleigh quotient]] to obtain increasingly accurate [[eigenvalue]] estimates.

Rayleigh quotient iteration is an [[iterative method]], that is, it delivers a sequence of approximate solutions that [[Limit of a sequence|converges]] to a true solution in the limit. Very rapid convergence is guaranteed and no more than a few iterations are needed in practice to obtain a reasonable approximation.  The Rayleigh quotient iteration algorithm [[rate of convergence|converges cubically]] for Hermitian or symmetric matrices, given an initial vector that is sufficiently close to an [[EigenVector|eigenvector]] of the [[Matrix (mathematics)|matrix]] that is being analyzed.