NRnum {lmfor}

Solve a Systems of Nonlinear Equations Using the Newton's Method

Description

Solves a system of equations of form f_1(x) = 0,f_2(x) = 0,...,f_p(x) = 0 for vector x using the multidimensional version of the Newton-Raphson algorithm. The gradients are solved numerically within the function using R-function numericDeriv.

Usage

NRnum(init, fnlist, crit = 6, ...)

Arguments

init

vector of initial values for x.

fnlist

list of R-functions for f_1(x), f_2(x), ..., f_p(x) each function gets a vector-valued argument x and returns a scalar value.

crit

Convergence criterion. Stop iteration when (|f_1(x)|+|f_2(x)|+...+|f_p(x)|<crit).

...

Other arguments passed to the functions of fnlist

Value

A list of components

par

the value of vector x in the solution

crit

the value of the convergence criterion at the solution

If estimation fails (no solution is found during 100 iterations), both elements of the solution are NA's.

Author(s)

Lauri Mehtatalo, <[e-mail]>

See Also

Function NR.

Examples

# Moment-based recovery of Weibull parameters
mu<-14
mu2<-210
muf<-function(theta) theta[2]*gamma(1+1/theta[1])-mu
mu2f<-function(theta) theta[2]^2*gamma(1+2/theta[1])-mu2
functions<-list(muf,mu2f)
momrec<-NRnum(c(3,13),functions)
momrec$par