HE 611 – Computer Programming and Numerical Methods
Assignment I
1. Construct a six-place divided difference table for the function ( ) =
− 9 + 26 − 24
in the range 1.1 ≤ ≤ 1.9 for = 1.10, 1.15, 1.20, 1.30, 1.35, 1.45, 1.60, 1.75, and 1.9.
2. From the divided difference table in Problem (1), interpolate for (1.44) using: (a) two
points, (b) three points, and (c) four points. In each case use the closest points to x=1.44
3. Use appropriate Lagrange interpolating polynomials of degree one, two, and three to
approximate
(0.25)
if
(0.1) = 0.62049958, (0.2) = −0.28398668, (0.3) =
0.00660095, (0.4) = 0.24842440
4. Use Newton’s interpolatory divided-difference formula to construct interpolating
polynomials of degree one, two and three for the following data. Approximate the specified
value using each of the polynomials. (8.4) if (8.1) = 16.94410, (8.3) = 17.56492,
(8.6) = 18.50515, (8.7) = 18.82091