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A Newton-Raphson approach is known to have quadratic convergence, and to always converge for a convex objective function.
A great advantage of the N R algorithm is that it is proven to converge quickly in general (quadratic convergence).
which shows the quadratic convergence.
It remains to show the quadratic convergence.
This proves the quadratic convergence in norm.
Moreover, we have established quadratic convergence of the algorithm.
The quadratic convergence of Algorithm 3.1 is given below.
Quadratic convergence is also proved for the algorithms.
The following theorem gives the quadratic convergence of Algorithm 3.1.
We also show that this method has local quadratic convergence.
This is not like the usual quadratic convergence estimate.
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