Numerical Analysis, Fall 1999

Homework 3

Due October 11, 1999

p 101; Work either 10 or 11. Answer to 10 is 16.2121.

PC-matlab or Derive for Windows in Brown Hall are easy ways to obtain any required graph for this assignment.

In #10, show a copy of the graph of the function.

In #11, show a copy of the function which is to be minimized overlaid with its derivative.

Redo the programming assignment for Homework # 2 but replace the bisection algorithm with Method of False Position 2.5 on p 73. Use C++, PC-Matlab, or other approved language.

P 63, 1a and b modified where you are required to show how to obtain both g's by algebra from f.

p 64; Let g(x) = 2^-x on [1/3,1]. Show 1/3 <=g(x)<=1 for 1/3<=x<=1. Find a k as required by Theorem 2.2. Once the k is found, use Corollary 2.4(first conclusion) to estimate the number of iterations required to achieve 10^-4. Do not find the fixed point.

P75,6d Proceed as in example 1 on p68 by writing p_n = .... Then exhibit a table similar to Table 2.3 on p 68. For one table, start with 1.5 and in second table start with 3. Produce enough rows to provide a good approximation. Also attach a graph of the function as was asked in first problem.