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Math Help - Singular Jacobian in Newton-Raphson

  1. #1
    Newbie eigenvex's Avatar
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    Singular Jacobian in Newton-Raphson

    I'm using Newton-Raphson to solve a set of nonlinear equations in an optimization problem. At the optimal, the Jacobian is singular (and I know this to be true) - it's about a 100x100 matrix and 3 of the rows are zeros.

    Obviously, to perform the matrix inversion of the Jacobian I need it to be full-rank (Really want to avoid doing pseudoinverses or anything of the sort), but once one of the variables corresponding to the row of 0's reaches its optimal (0), the matrix cannot be inverted.

    Any ideas how to get around this problem? i thought about damping the Newton step so that these variables will be the last to reach their optimal value and by then the convergence criteria would be within its limits...but I'm not sure if this makes sense.
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  2. #2
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    Re: Singular Jacobian in Newton-Raphson

    I know you posted this problem long time ago, however I do not see any replies to it. I have the same problem and I found several pdf files in the internet about the "extended Newton-Raphson method" and it is supposed to overcome the singularity of the Jacobian. If you have (as I would expect) already found the answer, please let me know that I am on the right track. If not, good luck to you too.
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  3. #3
    Super Member ILikeSerena's Avatar
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    Re: Singular Jacobian in Newton-Raphson

    The Levenberg-Marquardt algorithm can minimize a problem even if the solution is singular.
    It will find a solution that is more or less closest to the initial guess.
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