COT4501 Spring 2012
Homework V
This assignment has seven problems.
The assignment is due in class on Thursday, March
29, 2012. There are seven regular problems and two computer problems (using MATLAB).
For written problems, you need to show your work and it is insufficient to just give the results
or answers. For the computer problems, turn in your results (e.g., graphs, plots, simple analy
sis and so on) and also a printout of your (MATLAB) code.
Problem 1 (15pts)
1. Suppose you are using an iterative method to solve a nonlinear equation
f
(
x
) = 0
for
a root that is illconditioned, and you need to choose a convergence test. Would it be
better to terminate the iteration when you find an iterate
x
k
for which

f
(
x
k
)

is mall, or
when

x
k

x
k

1

is small? Why?
2. If the errors at successive iterations of an iterative method are as follows, how would
you characterize the convergence rate?
(a)
10

2
,
10

4
,
10

8
,
10

16
, ...
,
(b)
10

2
,
10

4
,
10

6
,
10

8
, ...
,
3. Suppose you are using the bisection method to find a zero of a nonlinear function, start
ing with an initial bracketing interval
[
a, b
]
. Give a general expression for the number
of iterations that will be required to achieve an error tolerance of
tol
for the length of the
final bracketing interval.
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 Spring '08
 Davis
 Numerical Analysis, Nonlinear system, 10pts, Rootfinding algorithm, nonlinear equation

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