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MATH 436/536  HW 2
Due Wed February 22
nd
.
1)
Use the NewtonRaphson method to find all 4 of the roots of the function
I
x
x
I
x
x
I
x
f
5
4
7
)
2
(
)
(
2
3
4
+
+

+

=
to at least 15 digit accuracy.
2)
For one of the complex roots in problem 1, show that the NewtonRaphson method has
order of convergence which is 2, that is, in general each iteration of the method
doubles the number of digits of accuracy over the previous iteration.
3)
Plot all 4 Basins of Attraction with their Julia set (use at least 6 back iterations) for the
function
I
x
x
I
x
x
I
x
f
5
4
7
)
2
(
)
(
2
3
4
+
+

+

=
.
4)
Use the two variable system version of the NewtonRaphson method to solve the
system
36
)
9
(
)
7
(
2
2
=

+
+
y
x
and
49
)
10
(
)
5
(
2
2
=

+
+
y
x
for all 4 solutions.
Now plot
their 4
Basins of Attraction.
5)
Use the Bisection method to find all of the real solutions of the equation
5
.
1
)
sin(
2
3
+
=
x
e
x
accurate to at least 15 decimal places.
6)
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 Spring '08
 Ken
 Math

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