code for 2 dimesional newtons method.


by iceblits
Tags: code, dimesional, method, newtons
iceblits
iceblits is offline
#1
Mar5-12, 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
Phys.Org News Partner Science news on Phys.org
Going nuts? Turkey looks to pistachios to heat new eco-city
Space-tested fluid flow concept advances infectious disease diagnoses
SpaceX launches supplies to space station (Update)
Bill Simpson
Bill Simpson is offline
#2
Mar5-12, 12:18 PM
P: 972
Remembering the gradient from multivariable calculus might get you started.


Register to reply

Related Discussions
Newtons method? Calculus & Beyond Homework 2
Newtons Method - A little help Calculus & Beyond Homework 3
newtons method. Calculus 2
newtons method Calculus & Beyond Homework 3
newtons method Calculus 5