On 8/23/07, Alejandro Garzon <gtg100n at mail.gatech.edu> wrote:
> 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?
This is exactly the condition number blowup of residual into error:
|e| \le |A^{-1} r|
|e| \le |A^{-1}| |r|
which looks like the condition number of A.
Matt
> Thanks
> --
> Alejandro
>
>
>
>
>
--
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which
their experiments lead.
-- Norbert Wiener
