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 Post subject: Hermit polynom of intepolation
PostPosted: Sat, 16 May 2009 11:41:30 UTC 
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Knowing that a function f is define on [0, 3] and that
f(0) = 1, f(1) = 2, f′(1) = −1, f(3) = f′(3) = 0.

a) Estimate f(2) using Hermite interpolation polynom .

b)Estimate the maxim error possible from point a) knowing that:
f ∈C^5[0, 3] and |f^{(5)}(x)|≤ M on [0, 3].
The maxim error is dependent on M

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 Post subject: Re: Hermit polynom of intepolation
PostPosted: Sat, 16 May 2009 14:02:44 UTC 
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silviu wrote:
Knowing that a function f is define on [0, 3] and that
f(0) = 1, f(1) = 2, f′(1) = −1, f(3) = f′(3) = 0.

a) Estimate f(2) using Hermite interpolation polynom .

b)Estimate the maxim error possible from point a) knowing that:
f ∈C^5[0, 3] and |f^{(5)}(x)|≤ M on [0, 3].
The maxim error is dependent on M


Your work?

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\begin{aligned}
Spin(1)&=O(1)=\mathbb{Z}/2&\quad&\text{and}\\
Spin(2)&=U(1)=SO(2)&&\text{are obvious}\\
Spin(3)&=Sp(1)=SU(2)&&\text{by }q\mapsto(\mathop{\mathrm{Im}}\mathbb{H}\ni p\mapsto qp\bar{q})\\
Spin(4)&=Sp(1)\times Sp(1)&&\text{by }(q_1,q_2)\mapsto(\mathbb{H}\ni p\mapsto q_1p\bar{q_2})\\
Spin(5)&=Sp(2)&&\text{by }\mathbb{HP}^1\cong S^4_{round}\hookrightarrow\mathbb{R}^5\\
Spin(6)&=SU(4)&&\text{by the irrep }\Lambda_+\mathbb{C}^4
\end{aligned}


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