  The compensated quotient-difference (Compqd) algorithm is proposed along with
some applications. The main motivation is based on the fact that the standard
quotient-difference (qd) algorithm can be numerically unstable. The Compqd
algorithm is obtained by applying error-free transformations to improve the
traditional qd algorithm. We study in detail the error analysis of the qd and
Compqd algorithms and we introduce new condition numbers so that the relative
forward rounding error bounds can be derived directly. Our numerical
experiments illustrate that the Compqd algorithm is much more accurate than the
qd algorithm, relegating the influence of the condition numbers up to second
order in the rounding unit of the computer. Three applications of the new
algorithm in the obtention of continued fractions and in pole and zero
detection are shown.
