Smolyak's algorithm for weighted \(L_1\)-approximation of multivariate functions with bounded \(r\)th mixed derivatives over \(\mathbb R^d\) (Q2583235)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Smolyak's algorithm for weighted \(L_1\)-approximation of multivariate functions with bounded \(r\)th mixed derivatives over \(\mathbb R^d\) |
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Smolyak's algorithm for weighted \(L_1\)-approximation of multivariate functions with bounded \(r\)th mixed derivatives over \(\mathbb R^d\) (English)
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13 January 2006
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The paper is dedicated to the study of a numerical method for the weighted \(L_1\) approximation of functions on an unbounded domain \(\mathbb R^d\). The method under consideration is based on a one-dimensional algorithm using a piecewise polynomial interpolation whose precise parameters are chosen according to the smoothness properties of the given function and the weight function. This one-dimensional method is then extended to a multidimensional setting via the classical sparse grid technique of \textit{S. A. Smolyak} [Dokl. Akad. Nauk SSSR 148, 1042--1045 (1963; Zbl 0202.39901)].
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\(L_1\) approximation
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Smolyak's algorithm
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unbounded domain
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piecewise polynomial interpolation
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