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      Non-linear Transformations of Divergent and Slowly Convergent Sequences

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      Journal: Journal of Mathematics and Physics
      Publisher: Wiley-Blackwell

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          XXV.—On Bernoulli's Numerical Solution of Algebraic Equations

          A. C. Aitken (1927)
          The aim of the present paper is to extend Daniel Bernoulli's method of approximating to the numerically greatest root of an algebraic equation. On the basis of the extension here given it now becomes possible to make Bernoulli's method a means of evaluating not merely the greatest root, but all the roots of an equation, whether real, complex, or repeated, by an arithmetical process well adapted to mechanical computation, and without any preliminary determination of the nature or position of the roots. In particular, the evaluation of complex roots is extremely simple, whatever the number of pairs of such roots. There is also a way of deriving from a sequence of approximations to a root successive sequences of ever-increasing rapidity of convergence.
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            Vorlesungen über Differenzenrechnung

            Niels Erik Nörlund (1924)
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              Solving linear algebraic equations can be interesting

              George E. Forsythe (1953)
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                Author and article information

                Journal
                Title: Journal of Mathematics and Physics
                Publisher: Wiley-Blackwell
                ISSN: 00971421
                Publication date Created: April 1955
                Publication date (Print): April 1955
                Volume: 34
                Issue: 1-4
                Pages: 1-42
                Article
                DOI: 10.1002/sapm19553411
                SO-VID: c30f995e-59ba-45ef-90c4-a086cc75c96e
                Copyright © © 1955
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                http://doi.wiley.com/10.1002/tdm_license_1.1

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