Results 1 to 2 of 2

Math Help - jacobian matrix

  1. #1
    Newbie
    Joined
    May 2010
    Posts
    15

    Post jacobian matrix

    please help in understanding this problem and any help solving it.

    1) Consider the linear system Ax = b where
    A = [ 2.2 2] and b = [6.2] and the solution is x = [1]
    2 2.2 6.4 2

    If we want to apply the Jacobi Iteration to this linear system, what will be the splitting of A, i.e. what are the matrices M and N, corresponding to the Jacobi Iteration? Is the Jacobi Iteration guaranteed to converge to the true solution x? Justify your answer? If convergent, what is the rate of convergence? Apply the Jacobi Iteration with the starting guess x^(0) = [0 0] until
    the relative error between the true solution and the kth iterate is less than or equal to 10^(-5), i.e. until (||x - x^(k)||2 ) / (||x||2) <= 10^(-5). Plot how the entries of the kth iterate evolve, i.e. plot x1^(k) and x2^(k) throughout the iteration?

    2) Repeat the above steps for the Gauss-Seidel Iteration..

    thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor chiph588@'s Avatar
    Joined
    Sep 2008
    From
    Champaign, Illinois
    Posts
    1,163
    Quote Originally Posted by vedicmath View Post
    please help in understanding this problem and any help solving it.

    1) Consider the linear system Ax = b where
    A = [ 2.2 2] and b = [6.2] and the solution is x = [1]
    2 2.2 6.4 2

    If we want to apply the Jacobi Iteration to this linear system, what will be the splitting of A, i.e. what are the matrices M and N, corresponding to the Jacobi Iteration? Is the Jacobi Iteration guaranteed to converge to the true solution x? Justify your answer? If convergent, what is the rate of convergence? Apply the Jacobi Iteration with the starting guess x^(0) = [0 0] until
    the relative error between the true solution and the kth iterate is less than or equal to 10^(-5), i.e. until (||x - x^(k)||2 ) / (||x||2) <= 10^(-5). Plot how the entries of the kth iterate evolve, i.e. plot x1^(k) and x2^(k) throughout the iteration?

    2) Repeat the above steps for the Gauss-Seidel Iteration..

    thanks!
    Straightforward: Jacobi method - Wikipedia, the free encyclopedia
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Jacobian Matrix
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: September 7th 2011, 04:39 PM
  2. Eigenvectors of a Jacobian matrix
    Posted in the Advanced Applied Math Forum
    Replies: 4
    Last Post: November 21st 2009, 08:00 AM
  3. jacobian matrix. derivatives
    Posted in the Calculus Forum
    Replies: 3
    Last Post: September 27th 2009, 03:10 PM
  4. Jacobian matrix exercise
    Posted in the Calculus Forum
    Replies: 3
    Last Post: August 2nd 2009, 12:46 AM
  5. inverse of a jacobian matrix
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: November 27th 2008, 04:34 PM

Search Tags


/mathhelpforum @mathhelpforum