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Nonlinear Numerical Methods and Rational Approximation II pp 269–282Cite as

On the Efficiency of Linear But Nonregular Sequence Transformations

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Part of the book series: Mathematics and Its Applications ((MAIA,volume 296))

Abstract

Regular matrix transformations, which satisfy the conditions of the theorem of Toe­plitz, have many advantageous theoretical properties, but they are at most moderately powerful. Theoretically, nonlinear sequence transformations, which are nonregular, are not yet very well un­derstood, but they are frequently remarkably powerful. Consequently, in recent years the emphasis has been on nonlinear methods. However, the bad reputation of linear sequence transformations in general is not completely justified. By means of some examples it is demonstrated that linear sequence transformations can be constructed which are extremely powerful for special problems. The key to the success of these linear methods is that they are very well adapted to the problems, for which they were constructed, and that they are nonregular.

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Authors and Affiliations

  1. Institut fūr Physikalische und Theoretische Chemie, Universität Regensburg, D-93040, Regensburg, Federal Republic of Germany

    Ernst Joachim Weniger

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  1. Ernst Joachim Weniger
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Editors and Affiliations

  1. Department of Mathematics and Computer Science, University of Antwerp, Antwerp, Belgium

    Annie Cuyt

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© 1994 Springer Science+Business Media Dordrecht

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Weniger, E.J. (1994). On the Efficiency of Linear But Nonregular Sequence Transformations. In: Cuyt, A. (eds) Nonlinear Numerical Methods and Rational Approximation II. Mathematics and Its Applications, vol 296. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0970-3_23

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  • DOI: https://doi.org/10.1007/978-94-011-0970-3_23

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4420-2

  • Online ISBN: 978-94-011-0970-3

  • eBook Packages: Springer Book Archive

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