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Numerical Approximation to Roots

  1. Apr 27, 2010 #1
    1. The problem statement, all variables and given/known data
    I'm trying to find a root-finding method for a function
    [tex] f: \mathbb R^n \to \mathbb R [/itex]

    2. Relevant equations
    x is a root of f(x) if f(x) = 0

    3. The attempt at a solution
    There is lots of work done for this problem when n=1, and also lots of work done when [itex] f: \mathbb R^n \to \mathbb R^n [/itex]. It seems like there should be a Newton method that can be applied here, but it's not entirely obvious to me. I've had some results by using the generalized Moore-Penrose inverse on [itex] \nabla f [/itex] but it's not something I would like to depend on in general. Does anyone know if there's an algorithm for solving this?
  2. jcsd
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