Numerical Analysis I, Fall 2017 (http://www.math.nthu.edu.tw/˜ wangwc/)

Homework Assignment for Week 04

Due Tuesday, Oct 17, 1:20PM.

1. Section 2.4: Problems 7(a), 8, 9, 10, 12, 13, 14.

Remark: Problem 13 can be derived by way of quadratic approximation of x = f^{−1}(y) at (y, x) = (f(x_{n}), x_{n}) (as shown in the slides for the linear approximation).

2. Section 2.5: Problems 12(a), 14, 16.

3. In Example 1 of section 2.5, the condition in Theorem 2.14 is not satisfied. Nevertheless, one could still get faster convergence of p̂_{n} than p_{n}, but of the same order. Analyze Aitken’s Δ^{2} method to evaluate lim_{n→∞} \frac{p̂_{n} − p}{p_{n+2} − p}. Then verify your result numerically.