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

Preparation guide for Quiz 02

The exam problems will be closely related to your homework problems. Make sure you understand all of them.

1. Section 1.3: Read the Illustration on page 32 and 33 carefully. Understand the source of instability for recurrence formula.

2. Section 1.3: Study how to obtain rate of convergence numerically by means of scaled plot.

3. Section 1.3: Review the definition of ’rate, or order, of convergence O(β_{n})’ on p37. Note the difference with ‘converge to p of order α’ on page 78.

4. Section 2.1-2.2: Study how to estimate number of iterations needed for linearly convergent methods such as bisection and fixed point iteration.

5. Section 2.2: Study the method and convergence proof (Theorem 2.3, 2.4, Corollary 2.5) of fixed point iteration.

6. Section 2.2: Study how to modify (generalize) the fixed point iteration when it does not converge.

7. Section 2.3: Study the secant method and method of false position. In particular, how to get p_{n+1} from previous p_{n}’s.

8. Section 2.1-2.3: Review programming for bisection, fixed point iteration Newton’s method and secant method.