User:EGM6341.s11.TEAM1.Sujin.HW1

=Problem 4: Infinity Norms=

Given
for $$ x\epsilon\ [0,1] $$ and

for $$x \epsilon\ [0,1] $$

Find
1) Plot $$ f(x) \ $$ and $$ g(x) \ $$ 2) Solve for:

Solution
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1) Plot $$ f(x) $$ and $$ g(x) $$
(i)Plot $$f(x)=3x+5x^3\ $$  Matlab code: 

(ii)Plot $$g(x)=\sinh\ x$$  Matlab code: 

(iii)Plot $$f(x)-g(x)=(3x-2x^3)-(\sinh x)\ $$  Matlab code: 

2)Find infinity norms
$$ ||f(x)||_{\infin}=1.4142 $$

$$ ||g(x)||_{\infin}=1.1752 $$

$$ ||f(x)||_{\infin} - ||g(x)||_{\infin}=0.2390$$

$$ ||f(x) - g(x)||_{\infin}=0.7392$$ As a result, we can verify the property of 'Infinity norm' as presented in lecture note, (1) p.5.3. Ref: Lecture Notes [[media:nm1.s11.mtg5.djvu|Mtg 5 (d)]]
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Author --Sujin 00:26, 19 January 2011 (UTC)EGM6341.s11.TEAM1.JANG