[PDF] convergence criteria for newton raphson method

Convergence of Newton Raphson Method It converges if |f(x).f''(x)| < |f'(x)|2. Also, this method fails if f'(x) = 0.
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  • How do you know if Newton's method will converge?

    Let g be twice continuously differentiable on the interval (a, b) .
    Let r be the root of g. If r?(a,b) such that g(r)=0 and g?(r)?0, then there exists ?>0 such that Newton's Method will converge if started in the interval [r -?, r+?].

  • How do you know if Newton's method will converge?

    Although the Newton-Raphson iteration procedure is stable and converges quadratically (provided the initial estimate is reasonably close to the solution), it has the disadvantage that the tangent stiffness matrix requires computationally expensive inversion during each iteration.

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