How changes on coefficients affect the solution of the system

Hi,

Let the linear system **Ax**=**b**.

I am looking for literature describing how changes on coefficients matrix **A** affect the solution of the system **x**.

For example if the value of the (i,j) element is doubled how this will affect the solution **x**?

Are there standard techniques applying to any linear system?

The A matrix is not known a priori and is quite large (thousands of equations), so techniques involving analytic solutions won't be of any help