lmfor (version 1.2)

NRnum: Solve systems of equations using the Gauss-Newton algorithm

Description

Solves systems of functions of form \(f_1(x) = 0\),\(f_2(x) = 0\),... for vector \(x\) using the Gauss-Newton algorithm (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

A vector of initial values for x.

fnlist

a list of R-functions for \(f_1(x)\), \(f_2(x)\), ... the functions get a vector-valued argument \(x\) and return a scalar value.

crit

The maximum accepted value of the convergence criteria. The applied criteria is the sum of absolute function values at the solution (\(|f_1(x)|+|f_2(x)+...|\))

…

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.

See Also

Function NR.

Examples

# NOT RUN {
# 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
# }