Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)


The parameterized $SR$ algorithm for symplectic (butterfly) matrices

Author: H. Faßbender
Journal: Math. Comp. 70 (2001), 1515-1541
MSC (2000): Primary 65F15
Published electronically: June 27, 2000
MathSciNet review: 1836916
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information


The $SR$ algorithm is a structure-preserving algorithm for computing the spectrum of symplectic matrices. Any symplectic matrix can be reduced to symplectic butterfly form. A symplectic matrix $B$ in butterfly form is uniquely determined by $4n-1$ parameters. Using these $4n-1$ parameters, we show how one step of the symplectic $SR$ algorithm for $B$ can be carried out in $\mathcal{O}(n)$ arithmetic operations compared to $\mathcal{O}(n^3)$ arithmetic operations when working on the actual symplectic matrix. Moreover, the symplectic structure, which will be destroyed in the numerical process due to roundoff errors when working with a symplectic (butterfly) matrix, will be forced by working just with the parameters.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2000): 65F15

Retrieve articles in all journals with MSC (2000): 65F15

Additional Information

H. Faßbender
Affiliation: Zentrum Mathematik, Technische Universität München, 80290 München, Germany

PII: S 0025-5718(00)01265-5
Keywords: Symplectic matrix; eigenvalue problem; $SR$ algorithm
Received by editor(s): March 2, 1999
Received by editor(s) in revised form: November 17, 1999
Published electronically: June 27, 2000
Article copyright: © Copyright 2000 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia