Rayleigh Quotient Iteration is an iterative numerical method used for finding an eigenvalue and corresponding eigenvector of a matrix. It is particularly useful for finding the eigenvalue that is closest to a given initial estimate. This method can be seen as an extension of the standard power iteration and is more efficient, especially when searching for a dominant eigenvalue.
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Starting from a unit vector , Rayleigh quotient iteration sets , solvesand normalizes . The shift is updated from the new vector.