All course materials class lectures and discussions handouts homework

All course materials class lectures and discussions

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* All course materials (class lectures and discussions, handouts, homework assignments, examinations, web ma- terials) and the intellectual content of the course itself are protected by United States Federal Copyright Law, the California Civil Code. The UC Policy 102.23 expressly prohibits students (and all other persons) from recording lectures or discussions and from distributing or selling lectures notes and all other course materials without the prior written permission of Prof. Hector D. Ceniceros. 1
(b) Consider the equidistributed pointsxj=-1 +j(2/n) forj= 0, ..., n. Write a computercode that uses (a) to evaluate and plotL(n)(x) (evaluateL(n)(x) at a large number ofpoints ¯xto have a good plotting resolution, e.g. ¯xk=-1 +k(2/ne),k= 0, ..., newithne= 1000) forn= 4, 10, and 20. Estimate Λnfor these three values ofn.(c) Repeat (b) with the nodes given byxj= cos(n),j= 0, ..., n. Contrast the behavior ofL(n)(x) and Λnwith those corresponding to the equidistributed points in (b).3.(a) Implement the Barycentric Formula for evaluating the interpolating polynomial for arbi-

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