Algorithm 826

A code for computing the eigenvalues of a complex Hessenberg matrix is presented. This code computes the Schur decomposition of a complex Hessenberg matrix. Together with existing ScaLAPACK routines, the eigenvalues of dense complex matrices can be directly computed using a parallel QR algorithm.Thi...

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Bibliographic Details
Published in:ACM transactions on mathematical software 2003-09, Vol.29 (3), p.326-336
Main Author: Fahey, Mark R
Format: Article
Language:English
Online Access:Get full text
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Summary:A code for computing the eigenvalues of a complex Hessenberg matrix is presented. This code computes the Schur decomposition of a complex Hessenberg matrix. Together with existing ScaLAPACK routines, the eigenvalues of dense complex matrices can be directly computed using a parallel QR algorithm.This parallel complex Schur decomposition routine was developed to fill a void in the ScaLAPACK library and was based on the parallel real Schur decomposition routine already in ScaLAPACK. The real-arithmetic version was appropriately modified to make it work with complex arithmetic and implement a complex multiple bulge QR algorithm. This also required the development of new auxiliary routines that perform essential operations for the complex Schur decomposition, and that will provide additional linear algebra computation capability to the parallel numerical library community.
ISSN:0098-3500