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)


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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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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