Day 22 in Mat360

Today:

• Announcements:
  • Collect problems 2.6 -- I've got to do this!;) Give me your Mullers!

  • An alternate form of the interpolating polynomial suggests a slick (and even a recursive) way of calculating polynomial values: Neville's method
    • Derivation
  • section 3.3 worksheet

• Section 3.2:
  • section 3.2 summary

  • Neville gives us some insight into a procedure for calculating the coefficients of the interpolating polynomial.... The Newton form of the interpolating polynomial.

  • Let's start by motivating the coefficients of the Newton form.

  • Then we'll look at a few practical problems:
    • One of them I hate: the "Guess the pattern I'm thinking of" problem

      Construct the divided-difference table for #2 (following Table 3.7, p. 120).

      How can we show that there are an infinite number of "rules" fitting the data?

    • The other I love: fitting data of interest (in this case, my energy use for the last year).