Inverse, Shifted Inverse, and Rayleigh Quotient Iteration as Newton's Method

DOI10.1137/15M1049956zbMath1382.65105OpenAlexW2788852429MaRDI QIDQ3133142

J. P. Schafermeyer, Richard A. Tapia, John E. jun. Dennis

Publication date: 13 February 2018

Published in: SIAM Review (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/15m1049956

zbMATH Keywords

algorithmeigenvalueNewton's methodeigenvectorsymmetric matrixinverse iterationRayleigh quotient iterationinverse power methodshifted inverse iterationmultiplier substitution method

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15)

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Implicit algorithms for eigenvector nonlinearities, A least-squares/relaxation method for the numerical solution of the three-dimensional elliptic Monge-Ampère equation, Block Newton method and block Rayleigh quotient iteration for computing invariant subspaces of general complex matrices, Richard von Mises’ work for ZAMM until his emigration in 1933 and glimpses of the later history of ZAMM, A survey on the high convergence orders and computational convergence orders of sequences, An unconstrained global optimization framework for real symmetric eigenvalue problems, A Newton's method characterization for real eigenvalue problems, Numerical methods for nonlinear equations, How Many Steps Still Left to $x$*?

Cites Work

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