Re: linalg[leastsqrs] in Maple V R4

In article <1154264326.861799.211040@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
lcw1964 <leslie.wright@xxxxxxxxxxxxx> wrote:
I know that I am using an admittedly ancient version of the software,
but it suits my modest personal purposes for the most part.

I am wondering if anyone has has any experience with the leastsqrs
procedure, in either older or newer incarnations, only to discover that
it seems painfully inaccurate on repeat application.

I have tried to use linalg[leastsqrs] to find the least squares
solution of an fairly hefty sized overdetermined system, about 80
equatons in 16 unknowns. Repeat application on the exact same
matrix/vector input combination yields different results with the loss
of many if not most of the significant digits. I am not talking just a
few digits lost to accumulated rounding error, I am talking a couple of
dozen digits when Digits is set pretty high. The problem gets worse the
larger the linear system is, and using the 'optimize' argument seems to
slow things down and doesn' add any value.

This is driving me wonky. Is this a bug or a feature? Is it present in
newer versions of Maple? Would I be better off using Svd() and
computing the least squares solution myself from that output? I really
don't mind "black box" routines if they give reproducible results, and
linalg[leastsqrs] in my hands does not.

The LinearAlgebra package in more recent versions of Maple should be
quite a bit better than linalg at most number-crunching applications.
But I didn't see any significant difference between linalg[leastsqrs]
and LinearAlgebra[LeastSquares] on a random 80 x 16 problem. Could
you provide a specific example of the problem you're experiencing?

Robert Israel israel@xxxxxxxxxxx
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
.

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