Revision history [back]

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?

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?

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?