I am implementing an equation solver into Omicron.
If I have an equation on the form:
f(x) = 0
If quite easy to solve using Newton-Raphson's method. This part of the equation solver works fine.
This equation system is a bit trickier:
f(x,y) = 0
g(x,y) = 0
That should be possible to solve using a similar method. But as of yet, I haven't studied any multi-dimensional analysis, so could someone please help me with an algorithm?
And what about the general case:
f1(x1,x2,...,xn) = 0
f2(x1,x2,...,xn) = 0
fn(x1,x2,...,xn) = 0