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 Subject: "Obtaining Polynomial Approximations" Previous Topic | Next Topic
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Crodo guest
Aug-28-02, 10:26 PM (EST)

"Obtaining Polynomial Approximations"

 If f(x)=sinx over the interval 0>x>pi/2 is wanted to be approximated by g(x)=px (p is a constant) what value of p would you choose to make:int.pi/2->0 f(x)dx= int.pi/2->0 g(x)dx ?(int = integral, pi/2->0 = over interval 0 to pi/2)and then what value of p would you choose to make:the maximum value of |f(x)-g(x)| in the interval as small as possible?and to make:int.pi/2->0^2dx as small as possible??

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alexb Charter Member
806 posts
Sep-03-02, 09:06 AM (EST)    1. "RE: Polynomial Approximations"
In response to message #0

 >If f(x)=sinx over the interval 0>x>pi/2 is wanted to be >approximated by g(x)=px (p is a constant) what value of p >would you choose to make: >int.pi/2->0 f(x)dx= int.pi/2->0 g(x)dx ? This is trivial. Just carry out the integration inint((f - g)2)dxto obtain a quadratic polynomial in p. Find the minimum of the parabola.>and then what value of p would you choose to make: >the maximum value of |f(x)-g(x)| in the interval as small as >possible? This falls under the Chebyshev theorem. There will be three points where the maxumum is achieved. See, e.g. P. Davis, Interpolation and Approximation, ch 7.>and to make: >int.pi/2->0^2dx as small as possible??

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