🚀 go-pugleaf

"Jon G." <jon8338@peoplepc.com> wrote in message news:<a_Nmd.3184$pK6.1193@newsread2.news.atl.earthlink.net>...
> Root Finder viii.
> by Jon Giffen
> [long derivation snipped]
> EXAMPLE:
> 
> t^3+2t^2+t-4=0  t=1
> [short derivation snipped]
> t  = 0.6666+0.3866 = 1.0532 ~ 1

Strike Eight! You're outta here!

> then
> 
>        t^2 + 3t + 4
>       ------------------------------
> t-1/  t^3 + 2t^2 + t - 4
>        t^3 -  t^2
>        --------------------
>              3t^2 + t - 4
>              3t^2 -3t
>              -------------
>                    4t - 4
> 
> and the remaining roots are
> 
>      -3+/-{9-16|^(1/2)
> t = ----------------- = -1.5+/-1.3229i
>            2
> 
> Dividing t^3 by t^2,
> 
> t^3 = 0.6666+1.1599 = 2.2656
> -----------------------------
> t^2 = 1.3333+1.0825 = 2.4158
> 
> or
> 
> t = 0.9378 ~ 1

But 1 isn't a root of t^2 + 3t + 4.

> EXAMPLE
> 
> t^7+t-10=0  t=?
> [short derviation cut]
> Use t=1.405 in Newton's Method

There are plenty of results giving good places to start off Newton's
Method.

>                   2.218
> t[n+1]=1.405 - ------------ = 1.364
>                 7(1.405)^6+1
> 
> t^7+t-10
> (1.364)^7+1.364-10 = 0.1734 ~ 0

Strike Eight (A). 
     If this is truly your last version, then you're outta here!
     -- Christopher Heckman