The RISE algorithm for recursive eigenspace decomposition

A recursive method for generating the eigenvalues and eigenvectors of Hermitian matrices is presented. This algorithm is closely related to recursive/iterative Toeplitz eigenspace decomposition (RITE) and thus may appropriately be named recursive/iterative self-adjoint eigenspace decomposition (RISE), since it is formulated for the more general Hermitian matrix. RISE may be performed at a cost of O(n ³) multiplies per matrix order, while RITE requires O(4n³). It is demonstrated that RISE (as is also true with RITE) is numerically stable, and thus does not appreciably accumulate errors as the recursion progresses. Additionally, a variation of RITE is presented which allows the computation of the eigenvalues of successively smaller Hermitian Toeplitz matrices. The initial presentation of RITE only provided for the determination of the eigenvalues of successively larger matrices