The Orthogonal Rayleigh Quotient Iteration (ORQI) method
نویسندگان
چکیده
منابع مشابه
The Rayleigh Quotient Iteration
The Rayleigh Quotient Iteration (RQI) was developed for real symmetric matrices. Its rapid local convergence is due to the stationarity of the Rayleigh Quotient at an eigenvector. Its excellent global properties are due to the monotonie decrease in the norms of the residuals. These facts are established for normal matrices. Both properties fail for nonnormal matrices and no generalization of th...
متن کاملInverse, Shifted Inverse, and Rayleigh Quotient Iteration as Newton's Method
Two-norm normalized inverse, shifted inverse, and Rayleigh quotient iteration are well-known algorithms for approximating an eigenvector of a symmetric matrix. In this work we establish rigorously that each one of these three algorithms can be viewed as a standard form of Newton’s method from the nonlinear programming literature, followed by the normalization. This equivalence adds considerable...
متن کاملTwo-sided Grassmann-Rayleigh quotient iteration
The two-sided Rayleigh quotient iteration proposed by Ostrowski computes a pair of corresponding left-right eigenvectors of a matrix C. We propose a Grassmannian version of this iteration, i.e., its iterates are pairs of p-dimensional subspaces instead of one-dimensional subspaces in the classical case. The new iteration generically converges locally cubically to the pairs of left-right p-dimen...
متن کاملRayleigh Quotient Iteration for Nonsymmetric Matrices
Rayleigh quotient iteration is an iterative algorithm for the calculation of approximate eigenvectors of a matrix. Given a matrix, the algorithm supplies a function whose iteration of an initial vector, vQ , produces a sequence of vectors, vn . If the matrix is symmetric, then for almost any choice of v0 the sequence will converge to an eigenvector at an eventually cubic rate. In this paper we ...
متن کاملConvergence Analysis of Inexact Rayleigh Quotient Iteration
We consider the computation of the smallest eigenvalue and associated eigenvector of a Hermitian positive definite pencil. Rayleigh quotient iteration (RQI) is known to converge cubically, and we first analyze how this convergence is affected when the arising linear systems are solved only approximately. We introduce a special measure of the relative error made in the solution of these systems ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2003
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(01)00330-5