High dimensional polynomial interpolation on sparse grids |
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Authors: | Barthelmann Volker Novak Erich Ritter Klaus |
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Institution: | 1.3SOFT, Wetterkreuz 19a, D-91058, Erlangen, Germany E-mail: ;2.Mathematisches Institut, Universität Erlangen-Nürnberg, Bismarckstraße 1 1/2, D-91054, Erlangen, Germany E-mail: ;3.Fakultät für Mathematik und Informatik, Universität Passau, D-94030, Passau, Germany E-mail: ; |
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Abstract: | We study polynomial interpolation on a d-dimensional cube, where d is large. We suggest to use the least solution at sparse grids with the extrema of the Chebyshev polynomials. The polynomial
exactness of this method is almost optimal. Our error bounds show that the method is universal, i.e., almost optimal for many
different function spaces. We report on numerical experiments for d = 10 using up to 652 065 interpolation points.
This revised version was published online in June 2006 with corrections to the Cover Date. |
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Keywords: | multivariate polynomial interpolation sparse grids least solution universal method tractability 41A05 41A63 65D05 41A25 |
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