ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Tue, 16 Sep 2014 18:04:30 +0200Linear equations with errorshttps://ask.sagemath.org/question/24152/linear-equations-with-errors/I have a system of $n^2$ homogeneous linear equations in $n^2$ variables.
Each equation is sparse and only involves $2n$ variables.
I create a list of equations and use solve(). I only get the "all-zero" solution. This is because of inaccuracies in the equations. I know (from theory) that there is be a nonzero kernel.
So, I'd like to find an approximate solution. That is - a solution of norm 1, which "almost fulfills" the equations.
Behind the scenes I probably need the SVD decomposition of the matrix describing the equations (or at least, the input vectors corresponding to the small singular values).
> 1. Do I have to create a matrix to represent the equations, or can I use my equations directly?
> 2. Can it be a sparse matrix?
> 3. Do I have to use an SVD routine, or is there some convenient way to solve my problem directly?
> 4. Do you have an example of how to do it?orenTue, 16 Sep 2014 18:04:30 +0200https://ask.sagemath.org/question/24152/