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How to prove a strictly diagonally dominant matrix is convergent

  1. Nov 26, 2011 #1

    If A and b are given, I know how to use the Jacobi's method to find out whether or not A is convergent. But how should I prove that "Jacobi's method is convergent if A is diagonally dominant" using just those given letters and symbols?
  2. jcsd
  3. Dec 26, 2011 #2
    Here's a hint: Contraction Mapping Theorem.

    (you want to show that the largest eigenvalue of the matrix D^-1x(L + U) is less than 1, then you can use the contraction mapping from there).
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