#### CS 3414 Homework 2 Due 5:00 p.m., June 6, 2002

The following data is needed for Problems 1-6.
```     x | 0 1 2 3 4
-------------
y | 1 2 1 2 3
```
1. Find the power form of the polynomial of degree 4 that interpolates this data. Make a plot showing this function and the 5 data points.

2. Find the shifted power form of the interpolating polynomial, with shift c=2.0.

3. Find the Lagrange form of the interpolating polynomial.

4. Find the Newton form of the interpolating polynomial.

5. Find the piecewise linear spline that interpolates this data.

6. Find the cubic spline that interpolates this data. Use the Matlab spline function and use Matlab to make a plot of the resulting spline and the five data points.

7. Do Computer Problems 1 and 2 on page 170 of Cheney and Kincaid. Again, Matlab is probably your best bet (see the Matlab code available on-line).

8. Choose an interesting 2D curve and compute (and draw) a parameterized representation of that curve using cubic splines and Matlab. (See Problem Statement 2 and Section 7.2 of our text for more discussion of the idea of a parametric representation.) Draw your curve on graph paper first (and turn that in), identify the control points, and then compute the splines needed to smoothly reproduce the curve in Matlab. An interesting curve (e.g., one or more cursive letters) may require you to compute several splines, corresponding to each of the smooth pieces that make up the figure. Don't choose a figure that requires you to construct dozens of splines though!