Two-sided Grassmann–Rayleigh quotient iteration
نویسندگان
چکیده
منابع مشابه
Two-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 کاملTuned preconditioners for inexact two-sided inverse and Rayleigh quotient iteration
Convergence results are provided for inexact two-sided inverse and Rayleigh quotient iteration, which extend the previously established results to the generalized eigenproblem, and inexact solves with a decreasing solve tolerance. Moreover, the simultaneous solution of the forward and adjoint problem arising in two-sided methods is considered and the successful tuning strategy for preconditione...
متن کاملM ar 2 00 8 Two - 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 کاملThe 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 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 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: Numerische Mathematik
سال: 2009
ISSN: 0029-599X,0945-3245
DOI: 10.1007/s00211-009-0266-y