# Inverse iteration

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In numerical analysisinverse iteration is an iterative eigenvalue algorithm. It allows to find an approximate eigenvector when an approximation to a corresponding eigenvalue is already known. The method is conceptually similar to the power method and is also known as the inverse power method.

# 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 for all eigenvalue algorithms). Fortunately, very rapid convergence is guaranteed and no more than a few iterations are needed in practice. The Rayleigh quotient iteration algorithm converges cubically, given an initial vector that is sufficiently close to an eigenvector of thematrix that is being analyzed.

# Power iteration

From Wikipedia, the free encyclopedia
In mathematics, the power iteration is an eigenvalue algorithm: given a matrix A, the algorithm will produce a number λ (theeigenvalue) and a nonzero vector v (the eigenvector), such that Av = λv.
The power iteration is a very simple algorithm. It does not compute a matrix decomposition, and hence it can be used when A is a very large sparse matrix. However, it will find only one eigenvalue (the one with the greatest absolute value) and it may converge only slowly.