Optimale Approximation mit Nebenbedingungen an lineare Funktionale auf periodischen Funktionen

Knauff, W.; Kreβ, R.

doi:10.1007/bf01462268

Cited by 4 publications

(2 citation statements)

References 2 publications

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“…The authors of [1], [4], [5] have treated the above problem in different ways for some special cases relative to either the functional L or a space setting and nodal location in the complex region of that space. In this paper, the common linear algebra background for the results of the abovementioned articles will be treated and additional results given.…”

Section: K(xy) = ~N_opm(x)p~(y) X Y E B mentioning

confidence: 99%

On the optimal approximation of bounded linear functionals in Hilbert spaces of analytic functions

Paulik¹

1976

BIT

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Abstract.Optimal numerical approximation of bounded linear funetionals by weighted sums in Hilbert spaces of functions analytic in a circle KF, in a circular annulus Krl,r~ and in an ellipse Er 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 ~Ks or on the eonfoeal ellipse ~Es and in the interval [-1,1] for an arbitrary bounded linear functional are given expllci~Iy. They are expressed in terms of a complete orthonormal system in the Hilbert space.

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Section: K(xy) = ~N_opm(x)p~(y) X Y E B mentioning

confidence: 99%

On the optimal approximation of bounded linear functionals in Hilbert spaces of analytic functions

Paulik¹

1976

BIT

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“…Der fiir p=2 auftretende Fall eines Hilbertraumes liefert des weiteren neue Ergebnisse, da er sich von den in [7] bzw. [1,5] angegebenen R~iumen unterscheidet.…”

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Fehlernormen zur Quadratur analytischer Funktionen

Knauff

1977

Computing

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Zusammenfassung --AbstractFehlernormen zur Quaflratur analytischer Funktionen. FiJr mit Lp-Normen, 1 _< p_< ~, versehene R/iume aus analytischen Funktionenf (z) wird die Norm der von Quadraturformeln erzeugten Fehlerfunktionale berechnet. Dies orfolgt mit Hilfe einer passend gew/~hlten Integraldarstellung fiirf (z) durch die Auswertung eines bestimmten Integrals, welche ffir einige interessante Fglle explizit durchgeffihrt wird. Error Norms of Quadratures for Analytic Functions.For spaces of analytic functionsf (z) with Lp-norms, 1 ~< p -< 0% the norm of quadrature error functionals is evaluated. This is done with the aid of a suitable integralrepresentation forf (z) by means of calculation a definite integral which is carried out explicitly in some interesting cases.

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Interpolation Operators as Optimal Recovery Schemes for Classes of Analytic Functions

Golomb

1977

Optimal Estimation in Approximation Theory

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Optimale Approximation mit Nebenbedingungen an lineare Funktionale auf periodischen Funktionen

Cited by 4 publications

References 2 publications

On the optimal approximation of bounded linear functionals in Hilbert spaces of analytic functions

On the optimal approximation of bounded linear functionals in Hilbert spaces of analytic functions

Fehlernormen zur Quadratur analytischer Funktionen

Interpolation Operators as Optimal Recovery Schemes for Classes of Analytic Functions

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