CS 5351/CS 4365, Fall 2010, Test 2

Name: ___________________________________________________________

1. Assuming that the computer uses 2 decimal digits, compute the range of a + b * c, where a is in the interval [0.9, 1.1], b is in the interval [0.009, 0.011], and c is in the interval [10, 16], with appropriate round-offs.

2-4. Estimate the range of function (1 - x) * (2 + x) on the interval [-3, 0] by using the following methods:

• use the centered form;
• use the mean valued form;
• use affine arithmetic.

5. A decision maker has three alternatives:

• for the first alternative a1, the range of possible benefits is [10.0, 20.0];
• for the second alternative a2, the range of possible benefits is [0.0, 30.0];
• for the third alternative a3, the range of possible benefits is [-5.0, 30.0].
Find out which alternative will be selected by each of the following four decision makers:
• a pessimist, for whom α = 0;
• an optimist, for whom α = 1;
• a decision maker for whom α = 0.5.

6. Use the interval-based optimization algorithm to locate the maximum of the function f(x) = x - x2 on the interval [0, 0.8]. Divide this interval into two, then divide the remaining intervals into two again, etc. Stop when you get intervals of width 0.1.

7-8. Use the constraints method to solve the following two problems:

• find x1 and x2, both from the interval [-10, 10], that satisfy the system of equations x1 + x2 = 0 and x1 * (1 + x2) = 0.09;
• find x1 and x2, both from the interval [-10, 10], that satisfy the system of equations x1 + x2 = 0 and x1 * (1 + x2) = 10.

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