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Problems and Results in the Calculation of Extremal Fundamental Systems for Sphere and Ball

  • Manfred Reimer
Part of the International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique book series (ISNM, volume 90)

Abstract

Let ℙ(D) denote any space of real polynomial restrictions onto the compact set D ⊂ ℝr, r ∈ ℕ \{1} with finite dimension N. The nodes t1,...,tN ∈ D are called a fundamental system (with regard to ℙ) if the corresponding evaluation-functionals are linear independent in ℙ′. In this case the Lagrangians L1,...,LN ∈ ℙ are well-defined by
$${{L}_{j}}({{t}_{k}})={{\delta }_{j,k}}for j,k\in \{1,\ldots N\}$$

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References

  1. Linde, U., Reimer, M., Sündermann, B. Numerische Berechnung extremaler Fundamentalsysteme. To appear in Computing.Google Scholar
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  3. Reimer, M., and Sündermann, B. (1986) A Remez-type algorithm for the calculation of extremal fundamental systems for polynomial spaces over the sphere. Computing 37, 43–58.CrossRefGoogle Scholar
  4. Reimer, M., and Sündermann, B. (1987) Günstige Knoten für die Interpolation mit homogenen harmonischen Polynomen. Resultate der Mathematik 11, 254–266.Google Scholar
  5. Tricorni, F.G. (1955) Vorlesungen über Orthogonalreihen (Springer).Google Scholar

Copyright information

© Birkhäuser Verlag Basel 1989

Authors and Affiliations

  • Manfred Reimer
    • 1
  1. 1.Fachbereich MathematikUniversität DortmundDortmund 50Federal Republic of Germany

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