[SOLVED] MATH1426 - Numerical Analysis — Homework 3

Prof. Boris Houska
1. A function of the form satisfies
f(0) = 0
f(1) = 1
f(4) = 14
f(9) = 75
f(16) = 244,
Explain how to use divided differences for constructing f. What are a0,a1,a2,a3, and a4?
2. Write a computer code that interpolates the function at the points
−5, −4, −3, −2, −1, 0, 1, 2, 3, 4, 5
by a natural (piecewise cubic) spline p. Also compute the integrals
and
and interpret your result.
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