A Multishift, Multipole Rational QZ Method with Aggressive Early Deflation

The rational QZ method generalizes the by implicitly supporting subspace iteration. In this paper we extend introducing shifts and poles of higher multiplicity in Hessenberg pencil, which is a pencil consisting two matrices. result multishift, multipole iteration on block pencils allows one to stick real arithmetic for input pencil. combination with optimally packed aggressive early deflation as an advanced technique obtain efficient dense generalized eigenvalue problem. numerical experiments compare results state-of-the-art routines problem show that are competitive terms speed accuracy.