xn max f yj pn yj j 01m with

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Unformatted text preview: he minimization of E (x0 , x1 , . . . , xn ) := max |f (yj ) − Pn (yj )| . j =0,1,...,m with respect to x0 , x1 , . . . , xn . In this task, you are asked to empirically determine a good distribution of the nodes (one that makes the error E (x0 , . . . , xn ) small). When you finish this task, upload the best error and the corresponding nodes that you found to IVLE. The best three solutions will be posted in the Forum for sharing. 1 h1 2. We shall use notations that are consistent with Matlab. Let (xi , fi ) for i = 1, 2, . . . , n be given data (note that the index starts from 1 instead of 0 because indices of Matlab arrays start from 1). Let hi = xi+1 − xi for i = 1, 2, . . . , n − 1 be the spacing of the ith subinterval. Then, the n × n linear system that determines the coefficients {ci }i=1,2,...,n of a natural spline is (the blanks depict zeros) 0...
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