The Multishift <i>QR</i> Algorithm. Part II: Aggressive Early Deflation

Abstract

Aggressive early deflation is a QR algorithm deflation strategy that takes advantage of matrix perturbations outside of the subdiagonal entries of the Hessenberg QR iterate. It identifies and deflates converged eigenvalues long before the classic small-subdiagonal strategy would. The new deflation strategy enhances the performance of conventional large-bulge multishift QR algorithms, but it is particularly effective in combination with the small-bulge multishift QR algorithm. The small-bulge multishift QR sweep with aggressive early deflation maintains a high rate of execution of floating point operations while significantly reducing the number of operations required.