Assignment #4: Root Finding (cont’d), Polynomial Interpolation
Due date: Monday, October 11, 2010 (10:10am)
For full credit you must show all of your work.
1.
Illustrate each of the possible outcomes listed below, by giving an example of a function
and an initial estimate that will cause Newton’s method to:
a.
diverge to positive or negative infinity
b.
cycle endlessly without ever converging
c.
fail because of an attempt to divide by zero
d.
cycle for a while and then converge
e.
converge steadily but very slowly
f.
converge quickly
[Hint: you can get some ideas from examples given in class and from the problems at the
end of chapter 3]
2.
By hand, estimate a root of
f
(
x
) =
x
3
–
½
x
+ 1 by using two iterations of the Secant
Method, with
x
0
= 0 and
x
1
= 1.
Repeat using
x
0
= 1 and
x
1
= 0.
3.
Using Matlab, write a general purpose function
Secant
that uses the Secant Method to
locate a root of a predefined function
f
, given two initial starting points
x
0
and
x
1
.
[Let
f
be defined independently from
Secant
, and let
x
0
and
x
1
be parameters that are input by
the user.]
Use good programming practices to ensure that the program terminates
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 Spring '08
 MEYER
 Numerical Analysis, Polynomial interpolation, Secant method, Rootfinding algorithm

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