Christian H. Reinsch

This algorithm uses a rational variant of the QR transformation with explicit shift for the computation of all of the eigenvalues of a real, symmetric, and tridiagonal matrix. Details are described in [1]. Procedures tred1 or tred3 published in [2] may be used to reduce any real, symmetric matrix to tridiagonal form. Turn the matrix end-for-end if necessary to bring very large entries to the bottom right-hand corner.