A Cache‐Aware Implementation of the Spectral Divide‐and‐Conquer Approach for the Non‐Symmetric Generalized Eigenvalue Problem

Abstract

AbstractWe 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)