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Re: [SCICOMP] algoritme til pow(float, float);



--- "Morten S. Nielsen" <sslug@sslug> wrote:
> Preben Bohn <sslug@sslug> [000930 04:17]:
> > Umiddelbart tror jeg ikke at du kan finde en rækkeudvikling der kan gøre
> > det særlig godt, men følgende er egentligt sikkert også hurtiger (men
> > kan vist umiddelbart kun bruges for heltallige n):
> > 
> > Du ønsker at finde x=a^(1/n). Det svarer til at finde nulpunkt for
> > f(x)=x^n-a. Vi får at f'(x)=nx^(n-1). Newtons metode giver så: 
> > 
> > x_i+1=x_i-(x_i^n-a)/(nx_i^(n-1))
> > 
> > Iterér indtil konvergens.
> > 
> 
> Problemet her er at konvergensen er meget langsom fordi nulpunktet er et
> 5 dobbelt nulpunkt. Jo større n er jo langsommere går det. Jeg jeg kan ikke
> lige huske hvad man gør i sådanne tilfælde... Så hvis det ikke virker i 
> praksis er det derfor.

Man skifter til bisection, når Newton kører for langsomt.

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