Numerical Analysis, Fall 1998

Homework 3

Due October 12, 1998

p 101; Work either 10 or 11. Answer to 10 is 16.2121. 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. PC-matlab is an easy way to obtain such graphs. If you rather, you can download from http://ARCHIVES.MATH.UTK.EDU/software/msdos/calculus/mpp/ a nice dos plotting program written by math faculty at USNaval Academy. Just click on mpp.zip to download, unzip and from dos command, type mpp. Also some have used MathCad, Excel for plotting etc.

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. 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.