Interval Computations,
Test 1 for the course
CS 5351/CS 4365, Fall 2013

Name: ___________________________________________________________

1. What is the main problem of interval computations? Why is this problem useful in practice?

2-5. We want to estimate the range of a function (1 + x) * (2 − x) on the interval [0,2]. Do the following:

6. Use calculus to find the range of a function f(x1, x2) = (x1)2 − x1 * x2 − (1/2) * (x2)2 + x2 when x1 is in the interval [−1, 1], and x2 is in the interval [−2, 2]. For extra credit: use naive interval computations to estimate this range.

7. Use the interval-based optimization algorithm to locate the maximum of the function

f(x) = (1 + x) * (2 − x)
on the interval [0, 0.8]. Divide this interval into two, then divide each of the remaining intervals into two again, etc. Stop when you get intervals of width 0.1.

8-9. Use the constraints method to solve the following two problems:

10. Briefly describe the topic of your class project and what you have done so far.