The Padé-Rayleigh-Ritz method for solving large Hermitian eigenproblems
type: Item
instance of: scholarly article
title: The Padé-Rayleigh-Ritz method for solving large Hermitian eigenproblems
zbMATH Open document ID: 0852.65036
DOI: 10.1007/BF02142494
author: N. Emad
published in: Numerical Algorithms
publication date: 1996-12-05T00:00:00Z
review text: The method described uses Padé approximants and the Krylov sequence \(x, Ax, \dots, A^{m - 1} x\) to compute a few Ritz eigenvalues of a large sparse Hermitian matrix \(A\) of order \(n\). The method approximates the poles of \(((I - \lambda A)^{-1} x,x)\) by those of its Padé approximant of order \(m (\ll n)\). The relationship of the method to the Lanczos method is discussed, with special emphasis on stability and suitability for parallel computation.
reviewed by: Alan L. Andrew
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 65F50
Mathematics Subject Classification ID: 65Y05
zbMATH DE Number: 871280
zbMATH Keywords: Padé-Rayleigh-Ritz method
zbMATH Keywords: Padé approximants
zbMATH Keywords: Krylov sequence
zbMATH Keywords: Ritz eigenvalues
zbMATH Keywords: large sparse Hermitian matrix
zbMATH Keywords: Lanczos method
zbMATH Keywords: stability
zbMATH Keywords: parallel computation
MaRDI profile type: Publication
cites work: Q4049660
cites work: Q3666156
cites work: Q4692748
cites work: Q5510750
cites work: Q3868672
cites work: Parallel subspace method for non-Hermitian eigenproblems on the Connection Machine (CM2)
cites work: The Triangular Decomposition of Hankel Matrices
cites work: Variations on Arnoldi's method for computing eigenelements of large unsymmetric matrices
cites work: The Lanczos Biorthogonalization Algorithm and Other Oblique Projection Methods for Solving Large Unsymmetric Systems
cites work: An Algorithm for the Inversion of Finite Hankel Matrices
cites work: Q5674306
full work available at URL: https://doi.org/10.1007/bf02142494
OpenAlex ID: W2056842497
description: scientific article; zbMATH DE number 871280