Description

Lagrange interpolation
Using the barycentric form of the Lagrange interpolation polynomial, solve the following problems:
Problems:
1. The table below contains the population of the USA from 1930 to 1980 (in thousands of inhabitants):
1930 1940 1950 1960 1970 1980
123203 131669 150697 179323 203212 226505:
Approximate the population in 1955 and 1995.

2. Approximate p115 with Lagrange interpolation, using the known values for three given nodes.
3. Plot the graphics of the function and of the Lagrange interpolation polynomial that interpolates the function f at 21 equally spaced points in the interval [0;10]:
–
Facultative:
1. Consider the function f : [ 4; 2] !R; f(x) = cos(x) and the given nodes 0,4; 3:
a) Plot the fundamental interpolation polynomials
b) Compute the value of Lagrange interpolation polynomial at x = 6 using both the classical formula and the baricentric formula.
c) Plot the graphs of the function f and of the corresponding Lagrange interpolation polynomial.
d) Give two other sets of nodes in [ 4; 2] and plot the correponding Lagrange interpolation polynomials.
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2. a) Plot the graphs of the function and of the corresponding Lagrange interpolation polynomials of 4-th, 8-th and 14-th degrees:
b) Consider the Chebyshev zeros of the rst kind
i = 1;:::;n: Plot the same graphs as at a) using 15 nodes obtained by linear transformation :
c) Consider the Chebyshev zeros of the second kind
i = 0;:::;n 1: Plot the same graphs as at a) using 15 nodes obtained by linear transformation .
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