Algorithm to solve equation with Newton solution

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Hi,
can someone tell me where to find the algorithm to solve equation with Newton Solution. It is a iterative solution,
where we change from

f(x) = 0 [1]

to

x = g(x) [2]

and then guest a value, calculate the value , and then use it in the equation again. I can code to change from form(1) to form(2)with normal equation like

x2 - 2x + 1 = 0

but I cannot solve complex equation just like

log(sin(X)) = 0

Can someone tell me the algorithm to change from form (1) to form (2) in code C# or pseudo-code which deal with all kind of equation? Thanks in advance.

Posted 30-Dec-10 22:26pm

Ryo-kun0101

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Espen Harlinn · Answer 1 · 2010-12-31T00:13:00

Solution 1

Here is one solution in c++
http://acumensoftwareinc.com/TechNotes/NewtonRaphson/html/[^]

You'll find a full description here:
http://en.wikipedia.org/wiki/Newton%27s_method[^]

Regards
Espen Harlinn

Posted 31-Dec-10 0:13am

Espen Harlinn

Ryo-kun0101 · Answer 2 · 2011-01-03T16:08:00

Thanks Espen. I have already found the wikipedia link but the method is a little different. My question is not about Newton method but about how to implement my Newton-like method in C# or even pseudo code? I am stuck at how to change the function from the form

f(x) = 0 [1]

to

x = g(x) [2]

How can we code them? Specially when my function is not just simple like

x2 - 2x - 1 = 0

but can be VERY VERY COMPLEX like

log(sin(x^2)) = 0

If my method( I mean the way I change from form [1] to form [2] then guess a value and use it in the form [2] to have a new value, then use it in the function [2] again and again until the value stop changing) is not correct, can someone tell me how to present such a complex function in code C#? And how to code the calculating the differential with that fucntion? Please tell me cause I have no idea now.