I have a set of linear equations which can be presented as A(alpha,n) x(alpha)=b(alpha,n), where 'n' is the dimension of the square matric A.
For a particular value of "n" and "alpha", I can solve the unknown vector x. Further, I can differentiate Ax=b with respect to alpha to find out the rate of change of variable x with respect to alpha.
The above exercise reads, Ax'=b'-xA', which gives the unknown vector x', for a given value of alpha and n.
If I chose different values of n while fixing alpha=alpha0, the rate of change of x with alpha ( x' ) does not converge with 'n'. I noticed that x (alpha=alpha0) converges with n, also x(alpha=alpha0+ delta alpha) also converges with 'n'. I am interested in the query why x' does not converge, in spite of the fact that x converges? Any comments regarding the same are highly appreciated.