Can NNLS algorithms solve overdetermined systems with positive constraints?

AI Thread Summary
NNLS algorithms can effectively address overdetermined systems of linear equations with positive constraints, particularly when fitting experimental data. The challenge arises when using standard least squares methods, which may yield oscillations and negative coefficients that lack physical relevance. Specific algorithms tailored for non-negative constraints are available, such as the non-negative least squares (NNLS) method. Resources and code implementations for NNLS in C and Fortran can assist in solving these types of problems. Utilizing these specialized algorithms can lead to more accurate and meaningful results in data fitting scenarios.
Sergei_G
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Hello everyone,

I'd like to solve overdetermined system of linear equations (in fact to fit experimental data)
(like y1=C1*X11+C2*X12+...+Cm1*X1m)
y2=C1*X21+C2*X22+..+Cm*X2m
...
yn=C1*Xn1+C2*Xn2+...Cm*Xnm)
sometimes n>>m sometimes n>~m , yi and xij are known coefficients
and I know ab initio that all unknowns C1...Cm are positive. Are there specific algorithms developed for such problem? I tried to solve it with simplest least square, but I always get something like oscillations with increase of m - Positive C are compensated by negative C and fit becomes perfect but it does not have physical sence.

Thanks,

Sergei.
 
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