TU Wien:Computernumerik VU (Schranz-Kirlinger)/Übungen SS16/Beispiel 4

Lösung

$p'(x)=6*(1-x)^{5}*(-1)=6*(1-x)^{5}$

$\kappa _{x}=|{\frac {x*(1-x)^{5}+(-6)}{(1-x)^{6}}}|=|{\frac {-6x}{1-x}}|$

$\kappa (0.9)=|{\frac {-5.4}{0.1}}|=54$

Matlab Code

function [ ] = bsp4()

y1 = (1-0.9)^6;

y2 = 1-6*0.9+15*0.9^2-20*0.9^3+15*0.9^4-6*0.9^5+0.9^6;

y3 = 1+0.9*(-6+0.9*(15+0.9*(-20+0.9*(15+0.9*(-6+0.9)))));

sprintf('%s %0.25f %s %0.25f %s %0.25f','y1 = ', y1, 'y2 = ', y2, 'y3 = ', y3)

relError1a = abs((10^-6 - y1)/10^-6);

relError1b = abs(1-(10^6*y1));

relError2a = abs((10^-6 - y2)/10^-6);

relError2b = abs(1-(10^6*y2));

relError3a = abs((10^-6 - y3)/10^-6);

relError3b = abs(1-(10^6*y3));

sprintf('%s %0.15f %0.15f','rel. Error y1 = ', relError1a, relError1b)

sprintf('%s %0.15f %0.15f','rel. Error y2 = ', relError2a, relError2b)

sprintf('%s %0.15f %0.15f','rel. Error y3 = ', relError3a, relError3b)

end