# NRnum: Solve a Systems of Nonlinear Equations Using the Newton's... In lmfor: Functions for Forest Biometrics

## 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

 `1` ```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)|

## 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>

Function `NR`.

## Examples

 ```1 2 3 4 5 6 7 8``` ```# Moment-based recovery of Weibull parameters mu<-14 mu2<-210 muf<-function(theta) theta*gamma(1+1/theta)-mu mu2f<-function(theta) theta^2*gamma(1+2/theta)-mu2 functions<-list(muf,mu2f) momrec<-NRnum(c(3,13),functions) momrec\$par ```

### Example output

```Loading required package: stats4