Adding Aggressive Early Deflation to the Restructured Symmetric QR Algorithm

The QR algorithm is an algorithm for computing the spectral decomposition of a symmetric matrix [9]. Despite it’s high accuracy, other methods are often preferred for the symmetric eigenvalue problem due to the QR algorithm’s relatively poor performance [13]. In recent years, new techniques have arisen that dramatically improve its performance. The restructured symmetric QR algorithm, introduced in [13], seeks to increase the rate at which operations are performed, thus reducing execution time. Aggressive early deflation, introduced in [3], seeks to reduce the total number of operations performed. This paper investigates these two techniques and explores the addition of aggressive early deflation to the restructured symmetric QR algorithm.