Singularity in matrix when inverting in Matlab

Question

As data I get a matrix A but in my algorithm I need to work on its inverse. What I do is:

C = inv(A) + B;

Then in another line I update A. In the next cycles I also need (updated) A inverse, again for this algorithm. And so on. In the later cycles I get this:

Matrix is close to singular or badly scaled. Results may be inaccurate. RCOND = 1.425117e-019

or this:

Warning: Matrix is singular to working precision.

or this:

Warning: Matrix is singular, close to singular or badly scaled. Results may be inaccurate. RCOND = NaN.

Can you help me how to avoid such singularity? Matrix is squared always.

Answer 1

It definitely depends on what you are doing and what matrix A represents (in some cases there might be programming error causing A become singular). But if the singularity of A is unavoidable, you can use the Moore-Penrose pseudoinverse as an alternative to inverse matrix which has most of the properties of an inverse matrix (See it in wiki).

The equivalent command in Matlab would be pinv.

Answer 2

You'd get yelled at and downvoted if you tried to post this over at StackOverflow. ;-)

The problem might be with you use of the function inv, which has a spotty reputation in Matlab circles. Try this:

C = A\eye(size(A)) + B;

Do you still get warnings? The trick is that here I used the backslash operator \, mldivide, left matrix divide. This solves for the inverse of A by much more numerically stable, and often much faster methods. If you still had warnings you should check the rank of A and read up on solving systems of linear equations and pinv as @pm89 suggested.