Skew-symmetric differential qd algorithm is accurate

Differential qd (dqd) algorithm with shifts is probably the fastest algorithm which accurately computes eigen-values of symmetric tridiagonal matrices. Here we will construct an algorithm for computing eigenvalues of skew-symmetric matrices by using implicitly QR and symplectic QR factorizations. If we apply this algorithm onto tridiagonal skew-symmetric matrices, we obtain the skew-symmetric dqd algorithm. Here incorporation of shifts is a much harder then in symmetric case, and yet to be implemented. But, as we expect, our algorithm enjoys high relative stability. (c) 2004 WILEY-VCH Verlag GmbH & Co. KGaA. Weinheim.