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Need help with 1 part of the question reg Matlab

  1. Aug 6, 2008 #1
    Consider an n by n tridiagonal matrix A where there is 3 on the diagonal and -1 on both sub-and super-diagonal. For eg, when n=4 the matrix will be
    [3 -1 0 0]
    [-1 3 -1 0]
    [0 -1 3 -1]
    [0 0 -1 3]
    Let b be the vector where bi = 1/i.
    (a) For n=4 find the value of T for the Jacobi method and find ||T||∞.
    (b) Will the norm be any different for a large value of n? Give a reason for your answer.
    (c) For n=25, write a Matlab script file to perform 4 iterations of Jacobi method to estimate the solution of Ax=b. Use the zero vector for your first estimate.

    Answer:
    (a) T=
    [0 0.33 0 0]
    [0.33 0 0.33 0]
    [0 0.33 0 0.33]
    [0 0 0.33 0]

    Therefore, ||T||∞ = 2/3

    (b) No it will not because the max the row sum will ever be in tridiagonal matrix is 2/3.

    Now can anyone help me with part (c) please!!!!!!
     
  2. jcsd
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