Can NNLS algorithms solve overdetermined systems with positive constraints?

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Discussion Overview

The discussion centers on the application of non-negative least squares (NNLS) algorithms to solve overdetermined systems of linear equations, particularly in the context of fitting experimental data while ensuring that all unknown coefficients remain positive.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant, Sergei, describes the challenge of fitting an overdetermined system of equations where the coefficients must be positive, noting issues with oscillations in the least squares solution when using standard methods.
  • Another participant suggests that Sergei might find useful resources related to least squares with non-negative constraints, providing links to relevant documentation and search results.
  • A further reply offers additional resources, including links to C and Fortran implementations of NNLS algorithms.

Areas of Agreement / Disagreement

Participants have not reached a consensus on the effectiveness of NNLS algorithms for this specific problem, and there are multiple suggestions and resources provided without a definitive resolution to the initial query.

Contextual Notes

The discussion does not clarify the specific limitations or assumptions underlying the proposed algorithms or the mathematical formulations involved in the problem.

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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