# [R] Initial value choosing in nleqslv package

J C Nash pro|jcn@@h @end|ng |rom gm@||@com
Tue Nov 15 16:19:31 CET 2022

```A rather crude approach to solving nonlinear equations is to rewrite the
equations as residuals and minimize the sum of squares. A zero sumsquares
gives a solution. It is NOT guaranteed to work, of course.

I recommend a Marquardt approach  minpack.lm::nlslm or my nlsr::nlfb. You
will need to specify a function for the jacobian (derivatives of the residuals
w.r.t. the parameters) for the latter package, but it does handle bounds
correctly. Bounds in minpack.lm can be specified but I've a couple of failed
cases, though I'll caution that in this area the scaling is such that all
packages can be made to fail in some cases.

I can send the latest developmental version of the nlsr package with some
updates to make use of jacobians easier if you take that route.

JN

On 2022-11-15 02:49, ASHLIN VARKEY wrote:
> In my work, I use l-moments for estimation and obtain a system of
> nonlinear equations. I am using the 'nleqslv' package in the R- program to
> solve these equations but am struggling to choose initial values. Is there
> any criteria to choose initial values in this package or is there any other
> method to solve these equations?  My system of equations are given below.
>
>   simeqn=function(x){
>
>    y=numeric(4)
>
>    y[1]=x[1]*(((gamma(1+x[2])*gamma(x[3]-x[2]))/gamma(x[3]))+((gamma(1-
> x[2])*gamma(x[4]+x[2]))/gamma(x[4])))- 38353
>
>
> y[2]=x[1]*gamma(1+x[2])*((gamma(x[3]-x[2])/gamma(x[3]))-(gamma(2*x[3]-x[2])/gamma(2*x[3]))-(gamma(x[4]+x[2])/gamma(x[4]))+(gamma(2*x[4]+x[2])/gamma(2*x[4])))-
> 3759.473
>
>
> y[3]=x[1]*gamma(1+x[2])*((gamma(x[3]-x[2])/gamma(x[3]))-(3*gamma(2*x[3]-x[2])/gamma(2*x[3]))+(2*gamma(3*x[3]-x[2])/gamma(3*x[3]))+(gamma(x[4]+x[2])/gamma(x[4]))-(3*gamma(2*x[4]+x[2])/gamma(2*x[4]))+(2*gamma(3*x[4]+x[2])/gamma(3*x[4])))-
> 966.3958
>
>    y[4]=
> x[1]*gamma(1+x[2])*((gamma(x[3]-x[2])/gamma(x[3]))-(6*gamma(2*x[3]-x[2])/gamma(2*x[3]))+(10*gamma(3*x[3]-x[2])/gamma(3*x[3]))-(5*gamma(4*x[3]-x[2])/gamma(4*x[3]))-(gamma(x[4]+x[2])/gamma(x[4]))+(6*gamma(2*x[4]+x[2])/gamma(2*x[4]))-(10*gamma(3*x[4]+x[2])/gamma(3*x[4]))+(5*gamma(4*x[4]+x[2])/gamma(4*x[4])))-
> 500.952
>
>    y
>
> }
>
> 	[[alternative HTML version deleted]]
>
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