[R] solving cubic/quartic equations non-iteratively

[spencerg]

standard square root computation requires an iteration.  Spencer

Peter Dalgaard wrote:
> Mads Jeppe Tarp-Johansen wrote:
>   
>> To R-helpers,
>>
>> R offers the polyroot function for solving mentioned equations iteratively.
>>
>> However, Dr Math and Mathworld (and other places) show in detail how to
>> solve mentioned equations non-iteratively.
>>
>> Do implementations for R that are non-iterative and that solve mentioned
>> equations exists?
>>     
>
> As far as I know, we don't even have the quadratic...
>
> They can't be hard to implement, though. However, you may need to take
> care that non-iterative solutions are not necessarily more precise or
> even faster than iterative ones. There may be cancellation issues and
> the closed-form expressions can be complicated and involve slow function
> calls.
>
>
>