Dear all,(adsbygoogle = window.adsbygoogle || []).push({});

I have a question about root-finding. In fact my problem is about solving system of nonlinear equations but I have simplified my question as follows:

Suppose I would like to find the root of the following function by iteration:

[itex]y=f(x,p(x))[/itex]

If I can calculate the total derivative with respect to x, I can use Newton-Raphson method effectively. However, for some reason, I can't calculate the total derivative. I can calculate the partial derivative though.

I am using the naive method of finding the root by "partial derivative". To this end, in each iteration I replace p(x) by its value evaluated from the previous value of x, treating it as a constant, and apply Newton-Raphson method. Convergence is achieved in most cases but I'm not sure if this is the right way.

My question is:

1. Is there a theory behind this method? Is it related to fixed-point iteration?

2. Does the convergence depend on p(x)?

Your help would be appreciated,

Hassan

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# Root-finding by iteration

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