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
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.
 Spring '08
 MEYER
 Numerical Analysis, Polynomial interpolation, Secant method, Rootfinding algorithm

Click to edit the document details