Hybrid codes that combine elements of the QR and LR algorithms are des
cribed. The codes can calculate the eigenvalues and, optionally, eigen
vectors of real, nonsymmetric matrices. Extensive tests are presented
as evidence that, for certain choices of parameters, the hybrid codes
possess the same high reliability as the QR algorithm and are signific
antly faster. The greatest success has been achieved with the codes th
at calculate eigenvalues only. These can do the task in 15% to 50% les
s time than the QR algorithm.