Abstract
Optimal numerical approximation of bounded linear functionals by weighted sums in Hilbert spaces of functions analytic in a circleK r , in a circular annulusK r1,r2 and in an ellipseE r is investigated by Davis' method on the common algebraic background for diagonalising the normal equation matrix. The weights and error functional norms for optimal rules with nodes located angle-equidistant on the concentric circle∂K s or on the confocal ellipseϖE s and in the interval [−1,1] for an arbitrary bounded linear functional are given explicitly. They are expressed in terms of a complete orthonormal system in the Hilbert space.
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References
M. M. Chawla and V. Kaul,Optimal rules for numerical integration round the unit circle, BIT, 13 (1973), pp. 145–152.
P. J. Davis,Errors of the numerical approximation for analytic functions, Survey of numerical analysis, J. Todd, ed., McGraw-Hill, New York, 1962, pp. 468–484.
P. J. Davis,Interpolation and Approximation, Blaisdell Publishing Company, Waltham, Massachusetts-Toronto-London, 1962.
W. Knauff and R. Kress,Optimale Approximation Linearer Funktionale auf periodischen Funktionen, Numer. Math., 22 (1974), pp. 187–205.
W. Knauff,Optimale Approximation mit Nebenbedingungen an lineare Funktionale auf H 2(E ϱ)und L 2(E ϱ), Computing, 14 (1975), pp. 235–250.
H. Meschkowski,Hilbertsche Räume mit Kernfunktion, Springer Verlag, Berlin-Göttingen-Heidelberg, 1962.
A. Paulik,Optimale Approximation linearer Funktionale auf analytischen und harmonischen Funktionen, Dissertation, Göttingen, 1975.
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Paulik, A. On the optimal approximation of bounded linear functionals in Hilbert spaces of analytic functions. BIT 16, 298–307 (1976). https://doi.org/10.1007/BF01932272
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DOI: https://doi.org/10.1007/BF01932272