The C-RISE algorithm and the generalized eigenvalue problem

An order-recursive iterative algorithm (named the C-RISE algorithm, since it combines the C-RITE and RISE algorithms) is presented for the generalized eigendecomposition of a Hermitian pencil. An important feature is the inherent computational parallelism of the resulting algorithm, pointing to the potential for VLSI implementation. The order-recursive nature presents the potential for solving problems of an a priori unknown, adequate minimal size rather than a single maximum size only. It is shown that the recursive nature is not detrimental to numerical performance, as it is competitive with standard algorithms solving the single maximum size problem only