CS 510 Computer Problem: Computation of the roots of a polynomial
due 10/5/10
Your objective is to compute the roots (real and complex) of the polynomial
p
(
x
)=18
x
6

30
x
5
+5
x
4

23
x
3
+26
x
2

9
x
+1
to within absolute error
≤
10

10
, if possible. Use of Matlab is strongly encouraged. For each
successful Newton iteration, print out the corresponding Newton iterates
x
k
and
f
(
x
k
)va
lues
.
Provide an interpretation of your computational results, including observed convergence rates and
inferences about the multiplicities of the roots. Do you feel you attained the desired accuracy in
your computed roots? Note: You should turn in a copy of your program, though the important
thing here is the computational results it gives and your analysis of those results.
Notes: Since
p
(
x
) has even degree it must have an even number of real roots, perhaps not all
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 Fall '10
 Richter
 Numerical Analysis, Multiplication, Complex number, nested multiplication

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