Page 322 - Numerical Analysis Using MATLAB and Excel

Chapter 7 Finite Differences and Interpolation

7.10 Exercises

1. Express the given polynomial fx() below as a factorial polynomial px() , calculate the leading
differences, and then construct the difference table with h = . 1

5
4
3
fx() = x – 2x + 4x – x + 6
2. Use the data of the table below and the appropriate (forward or backward) Gregory−Newton
formula, to compute:

a. 50.2

b. 55.9

x 50 51 52 53 54 55 56

x 7.071 7.141 7.211 7.280 7.348 7.416 7.483

3. Use the data of the table below and Newton’s divided difference formula to compute:

(
a. f1.3 )
b. f1.95( )

x 1.1 1.2 1.5 1.7 1.8 2.0
y=f(x) 1.112 1.219 1.636 2.054 2.323 3.011

7−44 Numerical Analysis Using MATLAB® and Excel®, Third Edition
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