Degree of best approximation by trigonometric blending functions

Haussmann, Werner; Jetter, Kurt; Steinhaus, Bernd

doi:10.1007/bf01246949

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Since Dti= D'(d"t")t'f D't'f !Holds For All Ft C ( Q ) the O...1

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Cited by 14 publications

(2 citation statements)

References 8 publications

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“…Some exact error estimates for functions of two variables approximated by a mixed sum of operators of one variable are obtained in [14]. Results on optimal polynomial and optimal trigonometric blending approximation of functions of two variables were first obtained in [48] and [49], respectively. Reducing boundary-value problems for partial differential equations to a system of ordinary linear integro-differential equations (LIDE) was analyzed in [17,[41][42][43].…”

Section: Historical Essaymentioning

confidence: 99%

Methods of function approximation and modern computer-based technologies (Review)

Litvin

Сергиенко

2007

Cybern Syst Anal

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Section: Historical Essaymentioning

confidence: 99%

Methods of function approximation and modern computer-based technologies (Review)

Litvin

Сергиенко

2007

Cybern Syst Anal

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“…In the case ft C 1 ' 1 ( Q) n C22,r we have F1 ! = 0 and hence [8] f(x,y) (TDf)(x,y) = -a00 (f) +a'(f)(x)+a0'(f)(y)…”

Section: Since Dti= D'(d"t")t'f D't'f !Holds For All Ft C ( Q ) the O...mentioning

confidence: 99%

Accelerating Convergence of Univariate and Bivariate Fourier Approximations

Tasche¹

1991

Z. Anal. Anwend.

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Bögel Functions, Tensor Products and Blending Approximation

Badea

Cottin

Gonska³

1995

Mathematische Nachrichten

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For two compact metric spaces X and Y, we prove that the space of all bounded Bogel functions on X x Y is isometrically isomorphic with the completion of the blending function spacewith respect to a suitable norm. This solves a problem raised by G. FREUD. Here M ( Z ) and C ( Z ) denote the spaces of all bounded and continuous functions on the metric space Z , respectively. Applications are given to some problems in so-called blending approximation. All this is based on an abstract Jackson-type theorem in terms of the entropy numbers of X and Y and the mixed modulus of smoothness.

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Degree of best approximation by trigonometric blending functions

Cited by 14 publications

References 8 publications

Methods of function approximation and modern computer-based technologies (Review)

Methods of function approximation and modern computer-based technologies (Review)

Accelerating Convergence of Univariate and Bivariate Fourier Approximations

Bögel Functions, Tensor Products and Blending Approximation

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