4365/CS 5354 Data Processing Under Security and Privacy
Summer 2016, Test 1
1. Similarly to how we used Newton's method to design algorithms
for computing square root and cubic root, design an algorithm for
computing the logarithm x = ln(a) as a solution to the equation
ex = a.
2. Use the algorithm for computing 1/b that we had in class (and
that is implemented in the computers) to perform the few first
steps of computing the ratio 1 / 1.1.
3. Use numerical differentiation to compute the derivative of the
function x2 − x when x = 1.
4. Use linearization technique and your estimate for the
derivative to estimate the range of this function when x is in the
interval [0.9, 1.1].
5. Use naive interval computations to estimate the same range.
6. Use mean value form to estimate the same range.
7. Use Newton's method to solve the following system of non-linear
equations: x1 * x2 = 3,
x1 + x2 = 4.
Start with the first
= 1 and x2
= 2. One
iteration is good enough.
8. Find the point closest the origin on the line x1
= 1. In other words, find the values
for which the sum
the smallest possible value under the constraint x1
9. Explain what is k-anonymity, and why it is important. If k
increases, will we get more or less privacy protection? Explain