# Re: [R] Non-linear system of equations

From: Paul Smith <phhs80_at_gmail.com>
Date: Fri, 25 Apr 2008 10:57:49 +0100

> I am trying to estimate the parameters of a bimodal normal distribution using moments matching, so I have to solve a non-linear system of equations. How can I solve the following simple example?
>
> x^2 - y^2 = 6
> x – y = 3
>
> I heard about nlsystemfit, but I don't know how to run it exactly. I have tried the following code, but it doesn't really work:
>
>
> f1 <-y~ x^2-x^2-6
> f2 <-z~ x-x-3
> f <- list(f1=0,f2=0)
> nlsystemfit("OLS",f,startvals=c(0,0))

You could try the recent package BB by Ravi Varadhan. The code could be the following:

library(BB)

f <- function(x) {
x1 <- x
x2 <- x

F <- rep(NA, 2)

F <- x1^2 - x2^2 - 6
F <- x1 - x2 - 3

return(F)
}

p0 <- c(1,2)
dfsane(par=p0, fn=f,control=list(maxit=3000))

I got the solution:

x1 = 2.5
x2 = -0.5

Paul

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