A novel, blocked algorithm for the reduction to Hessenberg-triangular form

We present an alternative algorithm and implementation for theHessenberg-triangular reduction, essential step in the QZalgorithm solving generalized eigenvalue problems. Thereduction has a cubic computational complexity, hence,high-performance implementations are compulsory keeping thecomputing time under control. Our is of simplemathematical nature relies on connection betweengeneralized classical Via system andthe reduction single matrix to Hessenberg form, we areable get theoretically equivalent toHessenberg-triangular form. As result, can perform most thecomputational work by relying existing, highly efficient implementations,which make extensive use blocking. The accompanying error analysisshows that preprocessing iterative refinement benecessary achieve accurate results. Numerical results showcompetitiveness with existing implementations.