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Intervallfunktionale vom GAUSS‐LEGENDRE‐Typ
Author(s) -
Pittnauer Franz,
Reimer Manfred
Publication year - 1979
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19790870121
Subject(s) - mathematics , quadrature (astronomy) , gauss–jacobi quadrature , clenshaw–curtis quadrature , gauss–kronrod quadrature formula , tanh sinh quadrature , class (philosophy) , legendre polynomials , property (philosophy) , gauss , gaussian quadrature , mathematical analysis , pure mathematics , nyström method , integral equation , philosophy , engineering , epistemology , artificial intelligence , computer science , electrical engineering , physics , quantum mechanics
A general class of quadrature formulas is discussed where the usual point functionals are replaced by interval functionals. The quadrature formulas of this type with highest possible degree of exactness are minimizing a certain functional. This leads to an existence theorem for arbitrary weights, which must comply with some necessary condition only. Besides, this minimum property enables us to calculate the nodes of such quadrature formulas very effectively.