COMPUTER SCIENCE 349A
ASSIGNMENT #4
DUE MONDAY FEBRUARY 6, 2012
(in class)
1.
(a)
Write a MATLAB function M-file for Newton’s method corresponding to the
following pseudocode:
converge
to
failed
output
while
end
root
x
i
i
if
end
exit
root
x
if
root
i
output
x
f
x
f
x
root
while
i
heading
output
i
)
ε
,
,
x
newton (
oot
function r
←
+
←
<
−
′
−
←
≤
←
=
0
0
0
0
0
0
1
/
1
,
)
(
/
)
(
imax
1
imax
ε
Use the following (or similar)
MATLAB print statements.
fprintf ( ‘ iteration
approximation \n’)
fprintf ( ‘ %6.0f ‘, i ), fprintf ( ‘%18.10f \n’, root )
fprintf ( ‘ failed to converge in %g ‘, imax ), fprintf (‘
iterations \n ‘ )
HAND IN
a copy of your MATLAB M-file.
(b)
An oscillating current in an electric circuit is described by
)
2
cos(
9
t
e
i
t
π
−
=
,
where
t
is in seconds.
Determine all positive values of
t
such that
i
= 3.5 .
The solution
to this problem can be posed as determining the positive zeros of a function
)
(
x
f
.
Careful analysis of the graph of the function
)
(
x
f
shows that
)
(
x
f
has only one positive
zero, and it is in the interval [0, 1].
Use the MATLAB function M-file
newton
with
6
0
10
,
1
.
0
−
=
=
ε
x
and imax = 20
to solve the above problem.
Note that in MATLAB,
6
10
−
is 1e-6 (not 10e-6).
Note.
You will need to write MATLAB function M-files with headers something like

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