Floating-point versus Symbolic Computations in theQD-algorithm

The convergence of columns in the univariate qd-algorithm to reciprocals of polar singularities of meromorphic functions has often proved to be very useful. Any q-column corresponding to a “simple pole of isolated modulus” converges to the reciprocal of the corresponding pole. By performing an equivalence transformation of the underlying corresponding continued fraction and programming the new qd-like scheme so as to compute algebraic expressions, the difference in convergence behaviour between the “simple pole” case and the “equal modulus” pole case of the floating-point algorithm is eliminated. c © 1997 Academic Press Limited