Interpret the results of the following numerical experiment and draw some conclusions. a. Define p to be the polynomial of degree 20 that interpolates the function f(x) = (1 + 6x²)-¹ at 21 equally spaced nodes in the interval [-1, 1]. Include the endpoints as nodes. Print a table of f(x), p(x), and f(x) - p(x) at 41 equally spaced points on the interval. b. Repeat the experiment using the Chebyshev nodes given by x₁ = cos[(i-1)π/20] (1≤ i ≤21) c. With 21 equally spaced knots, repeat the experiment using a cubic interpolating spline.

Interpret the results of the following numerical experiment and draw some conclusions. a. Define p to be the polynomial of degree 20 that interpolates the function f(x) = (1 + 6x²)-¹ at 21 equally spaced nodes in the interval [-1, 1]. Include the endpoints as nodes. Print a table of f(x), p(x), and f(x) - p(x) at 41 equally spaced points on the interval. b. Repeat the experiment using the Chebyshev nodes given by x₁ = cos[(i-1)π/20] (1≤ i ≤21) c. With 21 equally spaced knots, repeat the experiment using a cubic interpolating spline.

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter2: Basic Linear Algebra

Section: Chapter Questions

Problem 15RP

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