Find Sample Solutions for Underdetermined Systems of Linear Equations

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SUMMARY

This discussion centers on generating sample solutions for an underdetermined system of linear equations consisting of 379 equations and 6325 unknowns. Participants suggest that while there are infinitely many solutions, obtaining a few non-negative solutions is feasible. Tools like Mathematica can handle such computations, but they are not free. The discussion emphasizes exploring free linear algebra software as a viable alternative for users without access to commercial tools.

PREREQUISITES
  • Understanding of linear algebra concepts, particularly underdetermined systems.
  • Familiarity with matrix operations and nullspace calculations.
  • Knowledge of non-negative constraints in linear equations.
  • Experience with mathematical software tools for linear algebra.
NEXT STEPS
  • Research free linear algebra software options for solving large systems of equations.
  • Learn about computing the basis of the nullspace using tools like MATLAB or Octave.
  • Explore methods for enforcing non-negativity in solutions to linear equations.
  • Investigate online platforms that may support large matrix computations.
USEFUL FOR

Mathematicians, data scientists, and engineers working with large systems of linear equations, particularly those seeking non-negative solutions in their computations.

ztepman
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I have a system of 379 linear equations and 6325 unknowns. Does anyone know of a tool that can generate some (non-negative) solutions that satisfy this system? I know there are infinitely many, but it would be useful just to have a few for my purposes.
 
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Why not just compute the basis of the nullspace of the resulting matrix and pick arbitrary elements in that nullspace? Adding the condition that the coefficients should be nonnegative shouldn't be too hard to enforce I think.

I don't think any online tool that will let you feed it such a huge matrix but I am sure there exists free software to do it, maybe look around for free linear algebra software? Mathematica can do it but isn't free, but perhaps you know someone that has a copy that can run the data for you?
 

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