Real fast structure-preserving algorithm for eigenproblem of complex Hermitian matrices
type: Item
instance of: scholarly article
title: Real fast structure-preserving algorithm for eigenproblem of complex Hermitian matrices
zbMATH Open document ID: 1299.65064
DOI: 10.1155/2013/438320
author: Jiangzhou Lai
author: Linzhang Lu
published in: Mathematical Problems in Engineering
publication date: 2014-11-24T00:00:00Z
review text: Summary: It is well known that the flops for complex operations are usually 4 times of real cases. In the paper, using real operations instead of complex, a real fast structure-preserving algorithm for eigenproblem of complex Hermitian matrices is given. We make use of the real symmetric and skew-Hamiltonian structure transformed by Wilkinson's way, focus on symplectic orthogonal similarity transformations and their structure-preserving property, and then reduce it into a two-by-two block tridiagonal symmetric matrix. Finally a real algorithm can be quickly obtained for eigenvalue problems of the original Hermitian matrix. Numerical experiments show that the fast algorithm can solve real complex Hermitian matrix efficiently, stably, and with high precision.
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 15B57
zbMATH DE Number: 6372337
Wikidata QID: Q59027560
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/438320
OpenAlex ID: W2043934001
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description: scientific article; zbMATH DE number 6372337