Singularity for inverse matrix

问题:

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.

回答1:

You can add some minute identity matrix to A:

A = A + small_coeff * eye(size(A));

so that resulting matrix will be sufficiently non-singular