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I want to know that if you are given a very complex equation g(x)=A(T). How could you solve for x, which is a function of variable T. To be more specific, I encounter a polylogarithmic function I need to solve numerically..


migration rejected from Aug 3 '14 at 12:22

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closed as unclear what you're asking by William, Jyrki Lahtonen, Tunk-Fey, amWhy, Mathmo123 Aug 3 '14 at 12:22

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question.If this question can be reworded to fit the rules in the help center, please edit the question.

Would Mathematics be a better home for this question? – Wouter Aug 3 '14 at 0:53
This is impossible to answer without being more specific. Numerical root-finding (which is what this is) is a huge topic. – Nathan Reed Aug 3 '14 at 2:08
As Nathan said, this is a big field. Are the roots complex? Are you interested in the complex roots? Do you know the derivative of g analytically? Can you evaluate g simply, or is just evaluating it a big endeavor (if it's an integral that lacks a closed form, for example)? Do you have good bounds on the roots, or is it a crap shoot? These are all really important to know before going about root finding. – webb Aug 3 '14 at 2:25
Computational Science SE might be a better fit, but I suspect they will want a lot more specific problem statement. – paisanco Aug 3 '14 at 2:28

I guess by complex equation you don't mean equation with complex variables but a polynomial. I have a solution for you. Take a value of T and find out A(T)=y. Now get x solving g(x)-y=0 using a bisection method (or some root finding algorithm). Do that for every x on the parameter space. Choose your initial values carefully. You may use some plotting software to decide them.


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