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iceblits

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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 can't get x to be a general matrix in the 2d example.

Any help at all with the coding or anything would be awesome