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Math Help - Diagonally dominant matrices, real-life example

  1. #1
    Member Mollier's Avatar
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    Diagonally dominant matrices, real-life example

    Hi, I was implementing the Gauss-Seidel iteration, and started reading about diagonally dominant matrices. Everywhere I read it says how these types of matrices often turn up in real-life applications such as in the finite-element method etc.

    I am yet to see an example though, and I was wondering if there is some "simple" real-life application where diagonally dominant matrices turn up?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Mollier View Post
    Hi, I was implementing the Gauss-Seidel iteration, and started reading about diagonally dominant matrices. Everywhere I read it says how these types of matrices often turn up in real-life applications such as in the finite-element method etc.

    I am yet to see an example though, and I was wondering if there is some "simple" real-life application where diagonally dominant matrices turn up?
    The covariance matrix of a vector of near independent RVs.

    The matrix form of the discretized Laplacian operator in 1D (see Abramowitz and Stegun 25.3.23 and 25.3.24)



    CB
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    Finite difference method for solving boundary value problem?

    Calculating natural cubic spline.
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