A Cache-Aware Implementation of the Spectral Divide-and-Conquer Approach for the Non-Symmetric Generalized Eigenvalue Problem |
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Authors: | Peter Benner Martin Köhler Jens Saak |
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Institution: | Computational Methods in Systems and Control Theory, Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstr. 1, 39106 Magdeburg |
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Abstract: | 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) |
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