# Math Help - five point formula....

1. ## five point formula....

f′′(x) = [f(x − h)−2f(x) + f(x + h) ]/h^2 − [(h^2/12)* f^(4th derivative) (z)]

where, x − h < z < x + h.

Suppose that the function values in the formula in the figure above contain round-off errors that are bounded in absolute value by A and that
|f^(4)(z)| ≤ M, x−h < z < x+h.
Derive a bound for the total error in terms of A, M and h....

Thanks for the help...

2. Originally Posted by Vedicmaths
f′′(x) = [f(x − h)−2f(x) + f(x + h) ]/h^2 − [(h^2/12)* f^(4th derivative) (z)]

where, x − h < z < x + h.

Suppose that the function values in the formula in the figure above contain round-off errors that are bounded in absolute value by A and that
|f^(4)(z)| ≤ M, x−h < z < x+h.
Derive a bound for the total error in terms of A, M and h....

Thanks for the help...
The maximum absolute value of the error:

$e\le 4A/h^2+(h^2/12)M$

and this because all of these errors can be independednt, and so in the worse case can just add.

CB