Description

1. To investigate the relationship between yield of potatoes, y; and level of fertilizer, x; an experimenter divided a eld into 5 plots of equal size and applied di⁄ering amounts of fertilizer to each. The recorded data are given in the table (in pounds).
x 1 2 3 4 5
y 22 23 25 30 28
a) According to Newton interpolation polynomial, approximate how manypounds of potatoes are expected from a plot to which 2.5 pounds of fertilizer had been applied.
b) Plot the data given in the table and the corresponding Newton interpo-
lation polynomial.
2. Consider the function f : [0;6] ! R; f(x) = esinx and 13 equidistant interpolation points. Plot the interpolation points, the function f and the Newton intepolation polynomial.

3. Approximate p115 with precision ” = 10 3; using Aitken s algorithm.
Facultative:
1. Consider the function f : [ 5;5] ! R; f(x) = sinx and 20 equidistant interpolation points. Plot the interpolation points, the function f and the Lagrange intepolation polynomial obtained using Aitken s algorithm with precision
” = 10 3:
2. Consider the function f : [ 1;1] ! R and n = 10 nodes in the inteval [ 1;1]:
a) Compute the Lebesque function at a given point x,
where li(x), i = 1;:::;n are the fundamental Lagrange polynomials.
b) Plot the function g for n equidistant nodes in [ 1;1]:
c) Plot the function g for n Chebyshev nodes of the rst kind, [ 1;1]; i = 1;:::;n.
Chebyshev nodes of the second kind, xi =
cos( n ) 2 [ 1;1]; i = 0;:::;n 1.
1