Results 1 to 2 of 2

Math Help - five point formula....

  1. #1
    Member
    Joined
    May 2008
    Posts
    102
    Awards
    1

    Post 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...
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by Vedicmaths View Post
    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
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] three-point formula for numerical differentiation
    Posted in the Advanced Applied Math Forum
    Replies: 1
    Last Post: March 4th 2010, 09:18 PM
  2. Replies: 0
    Last Post: November 12th 2009, 04:15 PM
  3. isolated point, Cauchy integral formula
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: November 11th 2009, 11:49 PM
  4. Formula For Rotating a Point about anotherPoint
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: August 20th 2009, 10:15 AM
  5. College Algebra Distance Formula and Mid point
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: August 26th 2008, 01:19 PM

Search Tags


/mathhelpforum @mathhelpforum