-2

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]
kannan D.S
  • 1,107
  • 3
  • 17
  • 44

1 Answers1

0

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]
Lutz Lehmann
  • 25,219
  • 2
  • 22
  • 51