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 April 29th, 2013, 02:42 PM #1 Newbie   Joined: Feb 2013 Posts: 26 Thanks: 0 Polynomial interpolation How can I find a formula for this polynomial interpolation question? Let $x_i= x_0 +ih, \ i = 0,1,2,3; \ h>0=$. Find a polynomial $p(x)$ of degree $\le 5$ for which $p(x_i)=f(x_i), \ i=0,1,2,3;$ $p'(x_0)=f'(x_0), \ p'(x_2)=f#39;(x_2),$ where $f(x)$ has a continuous derivative of any order in $\mathbb{R}$. Also, derive an error formula for $f(x)-p(x).$ What is the order of approximation for $x\in [x_0,x_3]?$ Any help will be greatly appreciated.

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