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- W96634548 abstract "A general recipe for high-order approximation of generalized functions is introduced which is based on the use of L2-orthonormal bases consisting of C ∞ -functions and the appropriate choice of a discrete quadrature rule. Particular attention is paid to maintaining the distinction between point-wise functions (that is, which can be evaluated point-wise) and linear functionals defined on spaces of smooth functions (that is, distributions). It turns out that “best” point-wise approximation and “best” distributional approximation cannot be achieved simultaneously. This entails the validity of a kind of “numerical uncertainty principle”: The local value of a function and its action as a linear functional on test functions cannot be known at the same time with high accuracy, in general." @default.
- W96634548 created "2016-06-24" @default.
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- W96634548 date "2007-01-01" @default.
- W96634548 modified "2023-09-23" @default.
- W96634548 title "Numerical Approximation of Generalized Functions: Aliasing, the Gibbs Phenomenon and a Numerical Uncertainty Principle" @default.
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- W96634548 doi "https://doi.org/10.1007/978-3-7643-7794-6_22" @default.
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