Numerical Analysis I, Fall 2014 (http://www.math.nthu.edu.tw/˜ wangwc/)

Homework Assignment for Week 03

1. Read the details about ‘loglog’, ‘semilogx’, ‘semilogy’ in matlab/octave. Typical convergence behavior, such as y_{n} = C_{1}n^{−k}, z_{n} = C_{2}α^{n}, where n denotes the number of iterations and C_{1} > 0, C_{2} > 0, k > 0 and 0 < α < 1 are some constants, will have distinct behaviors when you choose the correct scaling. That is, if you try to plot y_{n} or z_{n} versus n in one of the special scalings above, you will see a straight line. Try to analyze it and find the rate of convergence of

lim_{n→∞} ∑_{i=1}^{n} \frac{1}{i^{2}} = \frac{π^{2}}{6}

numerically by plotting the results in the correct scaling.

2. Section 2.2: Problems 2(b), 7, 12(a), 16, 24.

3. Section 2.3: Problems 16, 17(a,b), 19, 23(c).

4. Section 2.4: Problems 8, 9, 10, 12, 14.