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A Cache‐Aware Implementation of the Spectral Divide‐and‐Conquer Approach for the Non‐Symmetric Generalized Eigenvalue Problem
Author(s) -
Benner Peter,
Köhler Martin,
Saak Jens
Publication year - 2014
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201410390
Subject(s) - divide and conquer algorithms , computer science , eigenvalues and eigenvectors , linear subspace , scalability , function (biology) , implementation , sign (mathematics) , scheme (mathematics) , cache , algorithm , theoretical computer science , parallel computing , mathematics , pure mathematics , mathematical analysis , physics , quantum mechanics , database , evolutionary biology , biology , programming language
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 & Co. KGaA, Weinheim)