Blocked algorithms and software for reduction of a regular matrix pair to generalized Schur form
ACM Transactions on Mathematical Software (TOMS)
PARA '02 Proceedings of the 6th International Conference on Applied Parallel Computing Advanced Scientific Computing
Chasing Bulges or Rotations? A Metamorphosis of the QR-Algorithm
SIAM Journal on Matrix Analysis and Applications
| Hi-index | 0.00 |
The QR algorithm and its variants are among the most popular methods for calculating eigenvalues of matrices. Typical implementations chase bulges from top to bottom of an upper Hessenberg matrix. It is also possible to chase bulges from bottom to top. There are some situations in which it may be advantageous to chase bulges in both directions at once, in which case one needs a procedure for passing bulges through each other without mixing up the information that the bulges convey. This paper derives a procedure for passing bulges of arbitrary degree through each other. Experiments with a Fortran 90 program show that the procedure works well in practice for bulges of degree two.