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MATH 446 / OR 481
SAUER
SPRING 2010
Project 1
Applying the Bisection Method
in Double Precision
Your job is to ﬁnd the real root of
f
1
(
x
) = 10(1

cos 4
x
)(2 cos 2
x

4 cos
5
x
+ 6 cos
2
x
+ 3 cos
x
sin
2
2
x

12 cos
x
sin
4
x

4)
+32 cos
9
x

48 cos
6
x
+ 96 cos
3
x

72 cos
x

4
that lies between
0
and
1
. There is only one such root. Our fundamental ques
tion: If you calculate in double precision (as Matlab does automatically), can you
guarantee that your answers are correct to double precision?
1. Apply the Bisection Method four times to calculate the root, using starting
intervals
[0
,
1]
,
[0
.
1
,
1]
,
[0
.
2
,
1]
,
and
[0
.
3
,
1]
respectively. Calculate the root
to as many correct places as you can. For each starting interval, report the
Bisection Method’s best guess for the root, to as many decimal places as
you can. (You should use
format long
in Matlab to see plenty of deci
mal places.) Report your backward, or checking, error for each of the four
runs. (We are mainly interested in the order of magnitude of the backward
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This note was uploaded on 10/27/2010 for the course MATH 446 taught by Professor Staff during the Spring '08 term at George Mason.
 Spring '08
 Staff
 Math

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