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Der Quotienten-Differenzen-Algorithmus

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Summary

The quotient-difference (=QD) algorithm developed by the author may be considered as an extension ofBernoulli's method for solving algebraic equations. WhereasBernoulli's method gives the dominant root as the limit of a sequence of quotientsq (v)1 =s (v+1)1 /s (v)1 formed from a certain numerical sequences (v)1 , the QD-algorithm gives (under certain conditions) all the rootsλ σ as the limits of similiar quotient sequencesq (v)σ =s (v+1)σ /s (v)σ . Close relationship exists between this method and the theory of continued fractions. In fact the QD-algorithm permits developing a function given in the form of a power series into a continued fraction in a remarkably simple manner.

In this paper only the theoretical aspects of the method are discussed. Practical applications will be discussed later.

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Authors and Affiliations

  1. Institut für angewandte Mathematik der ETH, Zürich

    Heinz Rutishauser

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  1. Heinz Rutishauser
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Rutishauser, H. Der Quotienten-Differenzen-Algorithmus. Journal of Applied Mathematics and Physics (ZAMP) 5, 233–251 (1954). https://doi.org/10.1007/BF01600331

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  • DOI: https://doi.org/10.1007/BF01600331

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