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  3. in this problem, you can use the matlab program po

In this problem, you can use the Matlab program posted on course website and Canvas (also...

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Advance Math

  1. In this problem, you can use the Matlab program posted on coursewebsite and Canvas (also given in the lecture) that computes theinterpolation polynomial. We want to see how well a given functioncan be approximated by the interpolation polynomials. Let f be afunction. We divide the the interval [−0.6,0.6] into subintervalsof the same length h = 0.02. The gridpoints are −0.6 = x1 < x2< ... < x61 = 0.6. Take N = 61 points (x1,y1),...(xN,yN) onthe graph of f.

    1. (a) For f(x) = sinx, plot the graph of the interpolation P onthe interval [−0.6,0.6]. Plot f and all of P on the same graph (forexample, by using the command hold on). Does the interpolationpolynomial approximate well the function f on the interval [−0.6,0.6]?

    2. (b) The same questions as in Part (a) but for f (x) = 1+x .

    3. (c) We know that the error between f and P is estimated by

| f (x) − P (x)| ≤ max |f (n) | (∗)

n n−1 [a,b]
Let f (x) = 1 and [a, b] = [−0.6, 0.6]. Use Stirling approximationm√m! ≈ 1 (for large

1+x me m) to show that the right hand side of (∗) goes toinfinity as n → ∞.

Answer & Explanation Solved by verified expert
3.5 Ratings (544 Votes)
clear allclose allx and y values for finding thefunction for which interpolation have to dofuncxsinxfprintffunction for which interpolation have to do fxdispfuncall interpolating pointsz106000206figure1hold onplotz1funcz1hold onall node valuefprintfn x20600206 y2funcx2 Function for Newton Divide difference ValueNewtonFormlengthx2x2y2z1    See Answer
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