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On the norm of the hyperinterpolation operator on the unit ball. (English) Zbl 1307.65018

Summary: We obtain the asymptotic order of the operator norm of the hyperinterpolation operator on the unit ball \(\mathbb{B}^d\), \(d \geq 2\), with respect to the measure \(b_{d, \mu}(1 - |x|^2)^{\mu - 1 / 2} d x\), \(\mu \geq 0\), where \(b_{d, \mu} = \big(\int_{\mathbb{B}^d}(1 - |x|^2)^{\mu - 1 / 2} d x\big)^{- 1}\).

MSC:

65D05 Numerical interpolation
65D32 Numerical quadrature and cubature formulas

Software:

HyperCube; Hyper2d
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Full Text: DOI

References:

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