|x1-x2|<=?

[Alejandro Garzon]

Hi, I have found two aproximations x1 and x2 to the solution of a linear system
A*x=b by two different methods with the same relative residual "e". That is
|A*x1 - b| < e*|b| and |A*x2 - b| < e*|b|. For debugging purposes I want to know
if an upper bound for |x1 - x2| can be derived from the two inequalities above.
I have gone this far in trying to find it:

 From the triangle inequality

|A*x1 - b -(A*x2 - b)| <= |A*x1 - b| + |A*x2 - b| = 2*e*|b|,

eliminating the b's in the left hand side,

|A*(x1-x2)| <= 2*e*|b|,

Does anybody know if from here a condition of the form

|x1-x2| <= ?

can be derived?

Thanks
--
Alejandro