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N15 - ME 510 NUMERICAL METHODS FOR ME II Chebyshev...

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ME – 510 NUMERICAL METHODS FOR ME II g51g85g82g73g17g3g39g85g17g3g41g68g85g88g78g3g36g85g213g81g111 Fall 2007 Chebyshev Economization Problem: Find a three-term approximation for f (x) = cos(x) on [-1,1] in the form cos(x) = a + b x 2 + c x 4 Solution: Maclaurin Expansion: ... - ! 8 x + ! 6 x - ! 4 x + ! 2 x - 1 = (x) cos 8 6 2 Rewrite in terms of Chebyshev Polynomials using reciprocal relations: cos(x) = 0.7652 T 0 - 0.22981 T 2 + 0.00495 T
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