Some Considerations in Implementing the QZ Algorithm.

Some considerations in implementing the QZ algorithm for generalized matrix eigenvalue problems are considered in this paper. Specifically, a new algorithm is suggested for implementing the general Householder transformation a deflation algorithm is described for a singular triangular B with A in Hessenberg form finally specific upper bounds are given for the negligible 2,1 elements in the final reduction of the quasi-triangular 2 x 2 blocks having real eigenvalues to upper triangular forms. These improvements are designed for better efficiency of the algorithm and improved accuracy of the final results.