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About approximations of exponentials

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Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (AAECC 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 948))

Abstract

We look for the approximation of exp(A 1+A 2) by a product in form exp(x 1 A 1)exp(y 1 A 2)⋯exp(x n A 1) exp(ynA2). We specially are interested in minimal approximations, with respect to the number of terms. After having shown some isomorphisms between specific free Lie subalgebras, we will prove the equivalence of the search of such approximations and approximations of exp(A 1+⋯+A n). The main result is based on the fact that the Lie subalgebra spanned by the homogeneous components of the Hausdorff series is free.

Research supported by the CNRS GDR 1026 (MEDICIS) and the Computer Algebra Lab. (GAGE) at the École Polytechnique

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Authors and Affiliations

  1. Équipe “Analyse Algébrique”, Institut de Mathématiques, Université Pierre & Marie Curie, Case 247, 4 place Jussieu, F-75252, Paris cedex 05

    P. -V. Koseleff

Authors
  1. P. -V. Koseleff
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Gérard Cohen Marc Giusti Teo Mora

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© 1995 Springer-Verlag Berlin Heidelberg

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Koseleff, P.V. (1995). About approximations of exponentials. In: Cohen, G., Giusti, M., Mora, T. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 1995. Lecture Notes in Computer Science, vol 948. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60114-7_24

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  • DOI: https://doi.org/10.1007/3-540-60114-7_24

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60114-2

  • Online ISBN: 978-3-540-49440-9

  • eBook Packages: Springer Book Archive

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