A Novel Divisional Bisection Method for the Symmetric Tridiagonal Eigenvalue Problem

Wei Chu, Yao Zhao and Hua Yuan ()
Additional contact information
Wei Chu: School of Naval Architecture and Ocean Engineering, Huazhong University of Sciences and Technology, Wuhan 430074, China
Yao Zhao: School of Naval Architecture and Ocean Engineering, Huazhong University of Sciences and Technology, Wuhan 430074, China
Hua Yuan: School of Naval Architecture and Ocean Engineering, Huazhong University of Sciences and Technology, Wuhan 430074, China

Mathematics, 2022, vol. 10, issue 15, 1-22

Abstract: The embarrassingly parallel nature of the Bisection Algorithm makes it easy and efficient to program on a parallel computer, but with an expensive time cost when all symmetric tridiagonal eigenvalues are wanted. In addition, few methods can calculate a single eigenvalue in parallel for now, especially in a specific order. This paper solves the issue with a new approach that can parallelize the Bisection iteration. Some pseudocodes and numerical results are presented. It shows our algorithm reduces the time cost by more than 35–70% compared to the Bisection algorithm while maintaining its accuracy and flexibility.

Keywords: symmetric tridiagonal matrix; eigenvalue solver; matrix division; parallel algorithm (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/15/2782/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/15/2782/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:10:y:2022:i:15:p:2782-:d:881464

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().