## High dimensional polynomial interpolation on sparse grids.(English)Zbl 0944.41001

This paper deals with polynomial interpolation on a $$d$$-dimensional cube, where $$d$$ is large. The authors suggest to use the least solution at sparse grids with extrema of the Chebyshev polynomials. Obtained error bounds show that the method is universal, i.e., almost optimal for many different function spaces. Numerical results in dimension $$d=$$ 10 using up to 652 065 interpolation points are presented.
Reviewer: K.Najzar (Praha)

### MSC:

 41A05 Interpolation in approximation theory 41A63 Multidimensional problems 65D05 Numerical interpolation 41A25 Rate of convergence, degree of approximation

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