Newton raphson for multiple variables

Jun 19, 2012 at 12:06 PM


Suppose we have an equation like 

var func = TermBuilder.Power(x6,3)+TermBuilder.Power(10-y4,2)+TermBuilder.Power(x4-x2,2)+TermBuilder.Power(y4,2)-950;

or any other function containing multiple variables..

how do we solve it using newton raphson to find the values of the variable .

Note : func is obtained as a single equation after considering all the constraints and simplifying all equations. 



Jun 20, 2012 at 3:58 AM

Newton-raphson solves equations of the form f(x) = 0, where x is an n-dimensional variable and f produces an n-dimensional output... so you have exactly n equations with n variables. In your case you will have a single equation with many variables - which is unsolvable using Newton-Raphson.

If you want to solve a multi-dimensional problem such as specified above, you can use the method described here. Computing the Jacobian matrix is simply computing the gradient for every one of the n functions, so you can use AutoDiff to do it.