For the provided data set, write equations for calculating the polynomial interpolation of degree 4 and find the formula for f by hand.
x = [1, 2, 3, 4, 5]
y = f(x) = [5, 31, 121, 341, 781]
For the provided data set, write equations for calculating the polynomial interpolation of degree 4 and find the formula for f by hand.
x = [1, 2, 3, 4, 5]
y = f(x) = [5, 31, 121, 341, 781]
The pyramid of iterated differences is
5 31 121 341 781
26 90 220 440
64 130 220
66 90
24
You can extend the table by setting the last line constant 24
and computing backwards or you could read off the coefficients of the Newton interpolation polynomial. Anyway, the extended value table for x=-3..10
is
[61, 11, 1, 1, 5, 31, 121, 341, 781, 1555, 2801, 4681, 7381, 11111]