The fastest way to check if a sparse matrix is singular or not?

Dear All,

For a large sparse matrix A, how can I check in a fastest way if matrix A is singluar or not? The matrix has a dimension of 6000 x 6000. I know lu is fast, but I need to repeat this calculations many times for different matrix A.

Thanks a lot in advance.

Beson

Answer 1

[Matt J]

condest(A)

[Benson Gou]

@Matt. Thanks for your reply. But I think there must be a threshold to judge if martrix A is singular or not. How to decide the threshold? Thanks.

[Matt J]

The condition number calculated by condest measures how much error magnification you get when you try to invert the matrix when solving a linear equation

https://en.wikipedia.org/wiki/Condition_number#Matrices

The "threshold" that you are pursuing would be determined from the amount of error magnification that your specific application can tolerate (note that it is not possible to have zero error magnification). If the error magnification is greater than what you can tolerate, you would consider the matrix "singular".