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The compensated quotient-difference (Compqd) algorithm is proposed along withsome applications. The main motivation is based on the fact that the standardquotient-difference (qd) algorithm can be numerically unstable. The Compqdalgorithm is obtained by applying error-free transformations to improve thetraditional qd algorithm. We study in detail the error analysis of the qd andCompqd algorithms and we introduce new condition numbers so that the relativeforward rounding error bounds can be derived directly. Our numericalexperiments illustrate that the Compqd algorithm is much more accurate than theqd algorithm, relegating the influence of the condition numbers up to secondorder in the rounding unit of the computer. Three applications of the newalgorithm in the obtention of continued fractions and in pole and zerodetection are shown.

Accurate Quotient-Difference algorithm: error analysis, improvements and applications