Rayleigh quotient iteration

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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 must be repeated until it converges to an answer (this is true of all eigenvalue algorithms). Fortunately, very rapid convergence is guaranteed and no more than a few iterations are needed in practice. The iteration converges cubically for almost all initial vectors.

[edit] See also

• Power iteration
• Inverse iteration

[edit] References

• Lloyd N. Trefethen and David Bau, III, Numerical Linear Algebra, Society for Industrial and Applied Mathematics, 1997. ISBN 0-89871-361-7.