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| | I am Sherita from Fort Lauderdale. I love to play Viola. Other hobbies are Water sports.<br><br>My web site - [http://ghoulgamer.weebly.com league of angels review] |
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| The '''equioscillation theorem''' concerns the [[Approximation theory|approximation]] of [[continuous function]]s using [[polynomial]]s when the merit function is the maximum difference ([[uniform norm]]). Its discovery is attributed to [[Pafnuty Chebyshev|Chebyshev]].
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| == Statement ==
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| Let <math>f</math> be a continuous function from <math>[a,b]</math> to <math>\mathbf{R}</math>. Among all the polynomials of degree <math>\le n</math>, the polynomial <math>g</math> minimizes the uniform norm of the difference <math> || f - g || _\infty </math> if and only if there are <math>n+2</math> points <math>a \le x_0 < x_1 < \cdots < x_{n+1} \le b</math> such that <math>f(x_i) - g(x_i) = \sigma (-1)^i || f - g || _\infty</math> where <math>\sigma = \pm 1</math>.
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| == Algorithms ==
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| Several [[minimax approximation algorithm]]s are available, the most common being the [[Remez algorithm]].
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| == References ==
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| * [http://www.math.uiowa.edu/~jeichhol/qual%20prep/Notes/cheb-equiosc-thm_2007.pdf Notes on Notes on how to prove Chebyshev’s equioscillation theorem]
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| * [http://mathdl.maa.org/images/upload_library/4/vol6/Mayans/Contents.html Another The Chebyshev Equioscillation Theorem by Robert Mayans]
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| [[Category:Polynomials]]
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| [[Category:Numerical analysis]]
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| [[Category:Theorems in analysis]]
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Latest revision as of 21:12, 3 September 2014
I am Sherita from Fort Lauderdale. I love to play Viola. Other hobbies are Water sports.
My web site - league of angels review