Algorithm 1019: A Task-based Multi-shift QR/QZ Algorithm with Aggressive Early Deflation

The QR algorithm is one of the three phases in process computing eigenvalues and eigenvectors a dense nonsymmetric matrix. This paper describes task-based for reducing an upper Hessenberg matrix to real Schur form. also supports generalized eigenvalue problems (QZ algorithm) but this concentrates on standard case. adopts previous algorithmic improvements, such as tightly-coupled multi-shifts Aggressive Early Deflation (AED) , incorporates several new ideas that significantly improve performance. includes, not limited to, elimination synchronization points, dynamic merging previously separate computational steps, shortening prioritization critical path, experimental GPU support. implementation demonstrated be multiple times faster than multi-threaded LAPACK ScaLAPACK both single-node multi-node configurations two different machines based Intel AMD CPUs. built top StarPU runtime system part open-source StarNEig library.