4 votes

Method to calculate solution of a linear equation system?

There is no way because there is no solution to the given system with $x_2 \neq 0$. This is because the second block of the equation system reads $Ax_2 = 0$, which has no non-trivial solutions ...
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4 votes

Nullspace calculation of large matrix with rational numbers without round-off errors (exact)

Sagemath looks fast enough. Here is an example created by taking a 999x1000 random rational matrix and appending its column sums at the bottom, so that [1, 1, ... , 1, -1] is the kernel. ...
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3 votes
Accepted

Accurately Computing a Positive Vector in the Nullspace of a Matrix

Quick answer to summarize my comments. Keep in mind that a delicate point is the choice of the truncation threshold in the SVD (what is "numerically zero" and what is not). If you do not ...
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3 votes
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Finding null vectors of a parameter-dependent matrix

I have used the method you described for a similar problem. I found that a combination of your Newton iteration, along with Brent's method on minimizing the smallest singular value gave pretty good ...
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2 votes

Finding null vectors of a parameter-dependent matrix

The problem of finding singular points of a parameter-dependent matrix is called the nonlinear eigenvalue problem in the field of numerical linear algebra. I think you could benefit from using ...
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1 vote
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Calculate the intersection of two matrix kernels in MATLAB

In MATLAB, null([A; B]) will find an orthogonal basis for the intersection of the null spaces of A and B. It seems unlikely that you really want to find this basis, but it's not clear from your ...
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1 vote

Find a single vector in the null space

If your sparse matrix isn't too large and you can store it in memory, you could use a sparse (rank-revealing) QR (or LU, or SVD) factorization to determine the kernel of your matrix $A$. Alternately, ...
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