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Last data update: 2014.03.03

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

NRnum

R Documentation

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.

Author(s)

Lauri Mehtatalo, lauri.mehtatalo@uef.fi

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