#### CS 3414 Homework 5 Due 5:00 p.m., June 26, 2002

1. (20 pts) Do problem 6.1.5 (page 251) of Cheney and Kincaid.

2. (20 pts) Do problem 6.2.8 (page 267) of Cheney and Kincaid. Note that the problem says to use scaled partial pivoting (see pages 256 and following). You should show intermediate steps, including which row is selected as the pivot row at each step. Show the actual row interchanges, i.e., don't use the index vector idea.

3. (20 pts) Suppose you want to construct a polynomial of degree n-1 that interpolates a given set of n data points, where the given x values are evenly spaced in the interval [0,1]. (For example, if n=3, the points would be 0.0, 0.5, and 1.0.) Suppose further that you decide to use the standard power basis for your polynomial, i.e., your polynomial will look like

p(x) = a0 + a1 x + ... an-1xn-1

As you know, it is possible to set up a linear system B*alpha=y whose solution alpha gives you the n coefficients a0, ..., an-1. Write a Matlab program to construct the matrix B and compute its condition number, for n = 3, 4, ..., 10. Turn in a copy of your code and the output showing the condition numbers. (Note: use the matlab function cond() to compute the condition numbers).

4. (40 pts) Modify the parabolic2 code (described in Section 13.1) to simulate the bratwurst problem, as described in the problem statement and mathematical model handouts. Turn in a copy of your program. And turn in two plots: one showing time-to-cook as a function of radius R, for R in [1.5,3.0]; and the other plot showing temperature at the point x=0 vs. time, for the case R=3.0.