This preview shows pages 1–2. Sign up to view the full content.
Computer Model Formulation
Midterm Exam 1
February, 14, 2007
Closed books, notes, and computers.
Calculators should be used only for arithmetic calculations
(not for plotting or analytical derivations).
1. (20 points) Consider the following function.
4
3
2
1
0
1
2
20
15
10
5
0
5
10
15
20
x
y
(a) Using this graph, perform 2 iterations of the bisection method. The initial interval
has the following lower and upper boundaries:
x
l
= 1 and
x
u
= 2. Make sure to
clearly label the plot!
(b) Estimate the number (
n
) of the bisection method iterations needed to obtain an
approximation
x
(
n
)
r
to the root
x
0
with precision
e
n
=

x
(
n
)
r

x
0

<
10

6
. Assume
that the initial interval is the same as in part (a).
(c) Can a bracketing method converge to the root at
x
=

2? Why or why not?
(d) Consider the method of false position. If your initial interval is
x
l
=

4,
x
u
= 2,
to which of the two roots will the iterations converge?
1
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 02/07/2009 for the course COT 3502 taught by Professor Hawkins during the Spring '08 term at University of Florida.
 Spring '08
 Hawkins

Click to edit the document details