-------------------------------------> last change: 30mar01
### Multivariate polynomial interpolation: hyperinterpolation

Here is a list of relevant papers. Complete references can be found
in the
spline bibliography,
under the handle indicated (handles start with a percent sign).
Hyperinterpolation, introduced by Ian Sloan in %Sloan95, uses a quadrature
rule exact on Pi_{2n}, to approximate the coefficients, wrto to an o.n.
basis, of the least-squares approximant from Pi_n, thereby obtaining a linear
projector onto polynomials of total degree le n that uses only function
values and whose L_2 error is within a multiple of the best uniform error
achievable by approximants from Pi_n.
In more than one variable, the result is not actual interpolation; hence the
`hyper'.

%LeGiaSloan01 show that, for L_2 of the unit sphere in RR^r, and with
some restriction on the quadrature rule used, the max-norm of the resulting
projector grows only like O(n^{r/2-1}).