17 Sep
2011
17 Sep
'11
12:04 p.m.
On Sat, Sep 17, 2011 at 9:40 AM, Charles R Harris <charlesr.harris@gmail.com> wrote:
The Vandermonde matrix needs to be used for the fitting so nothing should be changed there.
I remember now where I heard this: http://people.maths.ox.ac.uk/trefethen/mythstalk.pdf Specifically, the statement: "Some well-known algorithms take O(n^2) operations (e.g. naïve Lagrange formula) or are exponentially unstable (e.g. Vandermonde matrices based on monomials x^k )." I wasn't sure whether to interpret that as the Vandermonde-based algorithm being flawed, or the polynomial fitting problem on an equidistant grid being ill-conditioned in general. Regards Stéfan