Homeworks for CS 5383, Summer 2006

May 31, 2006 (due June 1):

1. In class, we found the range of a simple function on given intervals by using its monotonicity. Find the range for a similar example.

2. In class, we showed how we can use derivatives to estimate the range. Use derivatives to find the range of the function selected in Part 1.

3. Assume now that your function is only given as a black box. Use numerical differentiation to find the range of your function.

June 1 (due June 8):

4. Write a program that, given a function, measured values, and upper bounds on measurement errors, computes the accuracy of the result of data processing.

June 8 (due June 9):

5. In class, we had a formula for computing the standard deviation of the result of data processing. Run a numerical example for two versions of this method: a version that uses analytical differential differentiation and a version that uses numerical differentiation.

June 8 (due June 12):

6. Write a program that, given a function, measured values, and standard deviations of measurement errors, computes the standard deviation of the result of data processing. This program should use numerical differentiation.

June 9 (due June 14):

7. Write a program that, given a function, measured values, and standard deviations of measurement errors, computes the standard deviation of the result of data processing. This program should use Monte-Carlo simulations.

June 9 (due June 16):

8. Write a program that, given a function, measured values, and upper bounds on measurement errors, computes the accuracy of the result of data processing. Your program should use Cauchy-based Monte Carlo simulations.

June 14 (due June 15):

9. Give an example of processing fuzzy inputs.

July 10 (due July 13):

10. Implement the basic Monte-Carlo algorithm for computing the probability of trust.

July 10 (due July 13):

11. Numerically test the scaling-based algorithm for computing the probability of trust when the original trust probabilities are close to 1.

July 13 (due July 17):

12. Run a constraints algorithm and prove that the system of equation y=x-x^2 and y=0.7 has no solutions when x is in the interval [0,1].

July 13 (due July 17):

13. Implement the scaling-based Monte-Carlo algorithm for computing the probability of trust.