Math 151A Final Exam
March 19, 11:30 am 2:30 pm, 2001 @UCLA
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10 problems
•
100 points
•
Please do any 8 problems
•
180 minutes
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Good Luck!
SCORE:
1
2
3
4
5
6
7
8
9
10
Total
1
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1. (10 points)
Short answer questions:
a Give the relation between errors
e
n
+1
and
e
n
, where
e
n
:=

p
n

p

, asso
ciated with Newton’s method for solving nonlinear equations. (You can
use a constant
C
to represent any derivative which occur in this relation.)
b As an approximation method, is numerical differentiation stable? why or
why not?
c A linear system
Ax
= 0 has a unique solution
x
= 0, does the system
Ax
=
b
has unique solution for any given
b
?
d Assume a given function
f
∈
C
[
a, b
]. How many points would you use to
construct a Lagrange polynomial of degree 10?
2. (10 points) Newton’s method is used to find a solution to
p
=
p

f
(
p
)
/f
′
(
p
)
based on an initial approximation
p
0
. Given the tolerance
TOL
and the maxi
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 Spring '08
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 Math, Numerical Analysis, linear system Ax, Math 151A Final

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