Problem

Why are the Chebyshev nodes generally better than equally spaced nodes in polynomial int...

Why are the Chebyshev nodes generally better than equally spaced nodes in polynomial interpolation? The answer lies in the term that occurs in the error formula. If x_i = cos[(2i + 1)π/(2n + 2)], then

for all x in [−1, 1]. Carry out a numerical experiment to test the given inequality for n = 3, 7, 15.

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Solutions For Problems in Chapter 4.2

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