I have this function:
function(x)
-0.3*x*exp(-(((log(x)+(0.03+0.3*0.3/2)*0.5)/(0.3*sqrt(0.5)))^2)/2)/(2*sqrt(2*pi*0.5))
+ 0.03*exp(-0.03*0.5)*pnorm(-(log(x)+(0.03-0.3*0.3/2)*0.5)/(0.3*sqrt(0.5)))
uniroot is giving the correct results.
> uniroot(f,c(0,10))
$root
[1] 0.7347249
$f.root
[1] -1.955740e-07
$iter
[1] 12
$estim.prec
[1] 6.103516e-05
The newton method is not generating good result.
> for( x in seq(0,8,1)) { z <- nleqslv(x,f); print(c(z$x,z$fvec))}
[1] NaN 1.340781e+154
[1] NaN 1.340781e+154
[1] 3.406704e+00 -5.608658e-09
[1] 3.340717e+00 -9.480243e-09
[1] 4.000000e+00 -5.470677e-11
[1] 5.000000e+00 -3.386274e-14
[1] 6.000000e+00 -3.559448e-17
[1] 7.000000e+00 -6.065006e-20
[1] 8.000000e+00 -1.581856e-22
In this case I am looking for largest value of 'x' such that f(x) >= 0
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