Summary
In a general Hilbert space of periodic functions numerical approximations with equidistant nodes for any bounded linear functional are given which are of minimal error norm in the class of approximations being exact for certain trigonometric polynomials. In examples optimal quadrature formulas with such side conditions are considered.
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Literatur
Knauff, W., Kreß, R.: Optimale Approximation linearer Funktionale auf periodischen Funktionen. Numer. Math.22, 187–205 (1974)
Golomb, M.: Approximation by Periodic Spline Interpolants on Uniform Meshes. J. Approximation Theory1, 26–65 (1968)
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Knauff, W., Kreß, R. Optimale Approximation mit Nebenbedingungen an lineare Funktionale auf periodischen Funktionen. Numer. Math. 25, 149–152 (1976). https://doi.org/10.1007/BF01462268
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DOI: https://doi.org/10.1007/BF01462268