At Mon, 19 Feb 2007 20:28:09 -0500 (EST), Rene Girard wrote: > "I think the dy contribution is trying to capture the rounding error > from terms like x+h which is O(|x|*DBL_EPSILON)," Is "dy" not rather > trying to express the round-off due to cancellation caused by taking > difference like "f(x+h) - f(x-h)" ? Note that in the expression for > "dy" we have max between absolute value of r3 and r5 which are > differences. I do not agree that the expression for "dy" should be > divided by h^2.
In machine arithmetic the difference f(xp=x+h)-f(xm=x-h) is not computed with a step of 2*h unless x+h and x-h are exactly representable. Due to rounding the step is xp-xh = 2*h + O(eps*x) where eps is the precision. I think that is the effect that was trying to be captured (incorrectly). -- Brian Gough Network Theory Ltd, Publishing Free Software Manuals --- http://www.network-theory.co.uk/ _______________________________________________ Help-gsl mailing list [email protected] http://lists.gnu.org/mailman/listinfo/help-gsl
