A Cache‐Aware Implementation of the Spectral Divide‐and‐Conquer Approach for the Non‐Symmetric Generalized Eigenvalue Problem. Issue 1 (December 2014)

• Record Type: Journal Article
• Authors: Benner, Peter; Köhler, Martin; Saak, Jens
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 14:Issue 1(2014)
• Page Start: 819
• Page End: 820
• Publication Date: 2014-12
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201410390
• Languages: English
• ISSNs: 1617-7061

Abstract

<abstract abstract-type="main" xml:lang="en"> <title>Abstract</title> <p>We propose a new implementation of the sign function based spectral divide‐and‐conquer method for the generalized non‐symmetric eigenvalue problem. The basic idea is to use the generalized matrix sign function to split the spectrum and the corresponding deflating subspaces and to build a recursive scheme on top of this. The method focuses on an extensive usage of scalable level 3 BLAS operations in order to achieve a good performance on modern computer architectures which makes it computationally superior to current implementations of the classical QZ algorithm. (© 2014 Wiley‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)</p> </abstract>