h3 hn2 2hn2 hn1

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Unformatted text preview: 0 2(h1 + h2 ) h2 h2 2(h2 + h3 ) .. . h3 .. . .. . .. . .. . hn−2 .. . 2(hn−2 + hn−1 ) 0 hn−1 1 c1 c2 c3 . . . . . . cn−1 cn = − f2 ) − − f1 ) − f3 ) − − f2 ) 3 2 . . . . . . 3 (fn − fn−1 ) − h 3 (fn−1 − fn−2 ) hn − 1 n− 2 0 3 (f3 h2 3 (f4 h The formulas to compute the bi ’s and di ’s are 1 hi (fi+1 − fi ) − (2ci + ci+1 ) for i = 1, 2, . . . , n − 1 hi 3 1 = (ci+1 − ci ) for i = 1, 2, . . . , n − 1. 3hi bi = di 1 3 (f2 h1 3 (f3 h . Task 1 1. Let f (x) = e−20x for x ∈ [−1, 1] and let x0 = −1, x1 = −0.9, x2 = −0.8, . . . , x19 = 0.9, x20 = 1 be twenty-one distinct points in [−1, 1]. The following code evaluates f at the nodes, computes the coefficients of interpolating polynomial P20 , and displays the maximum absolute error maxj =0,1,...,2×105 |f (yj ) − P20 (yj )|, where yj = −1 + 10−5 j...
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