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In numerical analysis, inverse iteration (also known as the inverse power method) is an iterative eigenvalue algorithm. It allows one to find an approximate eigenvector when an approximation to a corresponding eigenvalue is already known. The method is conceptually similar to the power method. It appears to have originally been developed to ...
Power iteration for (A − μ i I) −1, where μ i for each iteration is the Rayleigh quotient of the previous iteration. Preconditioned inverse iteration [12] or LOBPCG algorithm: positive-definite real symmetric: eigenpair with value closest to μ: Inverse iteration using a preconditioner (an approximate inverse to A). Bisection method: real ...
In mathematics, power iteration (also known as the power method) is an eigenvalue algorithm: given a diagonalizable matrix, the algorithm will produce a number , which is the greatest (in absolute value) eigenvalue of , and a nonzero vector , which is a corresponding eigenvector of , that is, =.
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 converges to a true solution in the limit ...
However, in practical large-scale eigenvalue methods, the eigenvectors are usually computed in other ways, as a byproduct of the eigenvalue computation. In power iteration, for example, the eigenvector is actually computed before the eigenvalue (which is typically computed by the Rayleigh quotient of the eigenvector). [11]
A pregnant woman is recovering in the hospital after she was stabbed multiple times by a pizza delivery driver over the size of her tip, according to reports. The incident happened on Sunday, Dec ...
In the long history of financial frauds, Enron ranks near the top of the list, with the once high-flying energy trading company suddenly unraveling in a web of lies and accounting sleight-of-hand.
The first numerical algorithm for computing eigenvalues and eigenvectors appeared in 1929, when Richard von Mises published the power method. One of the most popular methods today, the QR algorithm, was proposed independently by John G. F. Francis [18] and Vera Kublanovskaya [19] in 1961. [20] [21]