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High dimensional polynomial interpolation on sparse grids (2000)

Barthelmann, Volker ; Novak, Erich ; Ritter, Klaus

Springer

Advances in computational mathematics 12 (2000), S. 273-288

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ISSN: 1572-9044

Keywords: multivariate polynomial interpolation ; sparse grids ; least solution ; universal method ; tractability ; 41A05 ; 41A63 ; 65D05 ; 41A25

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: 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.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1023/A:1018977404843

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