CODEWITHSUNDEEP
matrixlinear-algebra
user1318499
user1318499

Reputation: 1354

Eliminate redundant equations from linear system

I have 1 or more equations and 3 unknowns. I want to reduce it to the minimum number of equations possible. There can be either 0, 1 or infinitely many solutions. In the 0 solution case I don't need the reduced system but just need to know that it's happening.

Gaussian elimination would do but everyone says it's numerically unstable. Maybe that doesn't matter for such a small system as long as you use pivoting? I also don't need row echelon form, so it's a bit overkill.

They say SVD is more stable but I can't see how to obtain the reduced set of equations from the U, Sigma and V matrices it produces. It also looks like overkill.

Is it possible (and if so, efficient) to detect the redundant equations and simply remove them without altering the others?

Upvotes: 0

Views: 2067

Answers (1)

Jirka
Jirka

Reputation: 4213

You can use QR-decomposition. See this answer to see how to use it to identify dependent vectors (note that it looks for dependence between columns, while you are probably looking for dependence between rows).

Upvotes: 0

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