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This assignment is about polynomial interpolation. 1) The user should be able to enter: a. A...

This assignment is about polynomial interpolation.
1) The user should be able to enter:
a. A function named f.
b. A number of points (nodes) with their respective values.
c. A point x0
2) The output should be:
a. A Newton Divided Differences polynomial (function of x) that approximates the function with agreement in the points.
b. An approximation of f(x0) by Newton Divided Differences polynomial.
c. The approximation absolute and relative errors.

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Answer #1

1.a. Because polynomial ncan be used to approximate complicated curves.1 The Error in Polynomial Interpolation
Let pn(x) be the polynomial of degree n interpolating the data
x x0 x1 · · · xn
y y0 y1 · · · yn
Assume that the data is given by a function y = f(x) with the property that
yi = f(xi) and xi ∈ [a, b] for i = 0, 1, · · · , n. The question that we consider here
is: how accurately does the polynomial pn(x) approximate the function f(x) at
any point x?

2.a.

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