Rayleigh-Ritz approximation for the linear response eigenvalue problem
type: Item
instance of: scholarly article
zbMATH Open document ID: 1305.65126
DOI: 10.1137/130946563
author: Lei-Hong Zhang
author: Jungong Xue
author: Ren-Cang Li
published in: SIAM Journal on Matrix Analysis and Applications
publication date: 2014-10-15T00:00:00Z
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 15A42
Mathematics Subject Classification ID: 65L15
Mathematics Subject Classification ID: 34L16
zbMATH DE Number: 6356196
zbMATH Keywords: linear response eigenvalue problem
zbMATH Keywords: eigenvalue approximation
zbMATH Keywords: Rayleigh-Ritz approximation
zbMATH Keywords: canonical angles
zbMATH Keywords: deflating subspace
zbMATH Keywords: error bounds
zbMATH Keywords: random phase approximation
zbMATH Keywords: smallest positive eigenvalue
MaRDI profile type: Publication
OpenAlex ID: W2050538573
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title: Rayleigh-Ritz approximation for the linear response eigenvalue problem
review text: One important question in random phase approximation is to compute a few eigenpairs associated with the smallest positive eigenvalues of the following eigenvalue problem: NEWLINE\[NEWLINE \mathcal{H}w:= \begin{bmatrix} A & B \\ -B & -A \end{bmatrix} \begin{bmatrix} u \\ v \end{bmatrix}= \lambda \begin{bmatrix} u \\ v \end{bmatrix}, NEWLINE\]NEWLINE where \( A, B \in \mathbb{R}^{n \times n}\) are both symmetric matrices and \( \begin{bmatrix} A & B \\ B & A \end{bmatrix} \) is positive definite. This paper is concerned with approximation accuracy relationships between a pair of approximate deflating subspaces and approximate eigenvalues extracted by the pair. The lower and upper bounds on eigenvalue approximation errors are obtained. They are useful in analyzing numerical solutions to linear response eigenvalue problem.
reviewed by: Mykhaylo Pahirya
description: scientific article; zbMATH DE number 6356196