Newton Square Root Method in Python
Previous version of this article had a grave mistake in the derivation part due to my carelessness with LaTeX. Thanks Sergei Zhgirovski for pointing it out.
In this article, we will talk about one of the basic algorithms for finding square roots: Newton Square Root Method.
Newtonian Optimization
Newtonian optimization is one of the basic ideas in optimization where function to be optimized is evaluated at a random point. Afterwards, this point is shifted in the negative direction of gradient until convergence.
Newton Square Root Method
Square root expression is rephrased as a parabola that can be optimized via Newtonian optimization. The same can be applied to higher order roots. Optimal point for this function is the square root for “a”. Let us implement this in Python.
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