[Numpy-discussion] Efficient orthogonalisation with scipy/numpy

[Anne Archibald]

2010/1/19 Charles R Harris <charlesr.harris at gmail.com>:
>
> Note that if you apply the QR algorithm to a Vandermonde matrix with the
> columns properly ordered you can get a collection of graded orthogonal
> polynomials over a given set of points.

Or, if you want the polynomials in some other representation - by
values, or in terms of some basis of orthogonal polynomials - you can
construct an appropriate Vandermonde-style matrix and use QR. (When I
tried this, switching from the power basis to the Chebyshev basis let
me go from tens to hundreds of polynomials, and now Chebyshev
polynomials are first-class objects.)

Anne