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Code for 2 dimesional newtons method. 
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#1
Mar512, 08:34 AM

P: 113

Hey,
I'm trying to figure out how to do newtons method in 2 dimensions. That is, I want it to take in an input of my initial matrix {x0,y0} and then follow the algorithm to find the solution to f1(x,y)=0, f2(x,y)=0. The algorithm is {x1,y1}={x0,y0}A^1*F{x0,y0} where A is the matrix of mixed partials and F{x,y} is the matrix of {f1,f2} evaluated at {x0,y0}. I'm new at mathematica so I'm having more trouble on the coding side than the logic side. I was able to figure out how to do the code for single variable newton's method, but I don't know how to let it take in a matrix as an input. I know that matrices are written with brackets, but I don't know how to let a function be a matrix. Like in the one dimensional case I had: g[x_] := x  f[x]/(D[f[t], t] /. t > x) but I cant get x to be a general matrix in the 2d example. Any help at all with the coding or anything would be awesome 


#2
Mar512, 12:18 PM

P: 1,037

Remembering the gradient from multivariable calculus might get you started.



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