Re: linalg[leastsqrs] in Maple V R4

lcw1964 wrote:
Robert Israel wrote:
It would be nice to know more about u and bb, but I think this is
what is happening: leastsqrs works by solving the system
(u^T u) x = u^T bb. I suspect that your matrix u^T u is
ill-conditioned (or perhaps singular), which can cause
numerical problems here.

This is definitely the issue.

With Digits:=30, I compute u'u, its inverse, and multiply the former by
the later. The result is a square matrix with diagonal elements close
to unity up to the 23rd or 24th digit, and off diagonal elements of the
order roughly 10^-19 to 10^-23 at best. With a well-conditioned matrix
at Digits:=30, I would expect these off diagonal elements to be of
order 10^-27 at the worst. There is a lot more going one here than
round off error.

The Svd path is the one I must take! Thanks for the insight.

Les


I suggest using Gram polynomials for polynomial least-squares
fitting. Ralston's book describes them. (For equally-spaced
abscissas and weights they become Chebyshev polynomials.)

You can find a quick on-line exposition of the general case
in

http://galileo.phys.virginia.edu/classes/551.jvn.fall01/551Notes.htm

under the link "Representation of Functions".

--
Julian V. Noble
Professor Emeritus of Physics
University of Virginia
.