numerical analisys question..

**transgalactic** · May 29th 2010, 03:00 AM

http://i48.tinypic.com/2yzd213.jpg

how they got g1 g2 g3
?

**CaptainBlack** · May 29th 2010, 03:10 AM

Originally Posted by transgalactic

http://i48.tinypic.com/2yzd213.jpg

how they got g1 g2 g3
?

They are just different rearrangemants of $x^3-x-5=0$ into the form $x=g(x)$ , presumably to show that formula iteration converges for some but not others.

$g_1(x)$ comes from the rearrangement $x=x^3-5$

$g_2(x)$ comes from the rearrangement $x^3=x-5$ , so $x= \sqrt[3]{x-5}$

$g_3(x)$ comes from the rearrangement $x(x^2-1)-5=0$ so $x=\frac{5}{x^2-1}$

CB

**transgalactic** · May 29th 2010, 03:31 AM

ok i solved a similar equation:
$x^3+2x^2+4-x=0$
$g1=x^3+2x^2+4$

why for g1 L=0.5
how to find L for other g
what is the meaning of L?

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