Lecture20101111_2

Lecture20101111_2 - The lagrange form is a direct way to...

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which goes through each n C 1 data point, with a polynomail of order . Given C 1 data points x 0 , y 0 , 1 , 1 $ ... $ , where no two j are the same, the interpolating polynomial in the lagrange form is a linear combination. p = > = 0 L where = ? k = 0, s K K Say = 2 (ie, 3 data points) = 0, 1, 2, we want to construct 2 2 = > = 0 2 = 0 0 C 1 1 C 2 2 = ? = 0, s 2 K K 0 = ? = 0, s 2 K 0 K = K 1 K 2 0 K 1 0 K 2 1 = ? = 0, s 2 K 1 K = K 0 K 2 1 K 0 1 K 2 2 = ? = 0, s 2 K 2 K = K 0 K 1 2 K 0 2 K 1 Take particular data 0 , 0 = 1, 1 , 1 , 1 = 2, 4 , 2 , 2 = 3, 9 = 1 2 2 K 5 C 6 1 = K 1 K 3 2 K 1 2 K 3 = K 1 2 K 4 C 3 2 = K 1 K 2 3 K 1 3 K 2 = 1 2 2 K 3 C 2 2 = 1 $ 1 2 2 K 5 C 6 K 4 2 K 4 C 3 C 9 $ 1 2 2 K 3 C 2 = 1 2 2 K 5 C 6 K 8 2 C 3 2 C 24 C 9 2 K 27 C 18 = 1 2 2 2 C 0 C 0 = 2 From online notes Theorem 3.2 Let f be a continuous function on a , b and let i = 0 be C 1 distinct points lying in , . Then a unique polynomial, of degree at most st = fx .
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This note was uploaded on 02/09/2011 for the course MATH 2051 taught by Professor Dr.a.wacher during the Fall '11 term at Durham.

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Lecture20101111_2 - The lagrange form is a direct way to...

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