Final Exam, Math 151A/3, Fall 2001, UCLA, 12/11/2001, 8am11am
NAME:
STUDENT ID #:
This is a closedbook and closednote examination. Please show all you work. Partial credit will
be given to partial answers.
There are 8 problems of total 100 points.
Time: 3 hours.
SCORE:
I
————–
II
————–
III
————–
IV
————–
V
————–
VI
————–
VII
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VIII
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Total
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I
Construct in 3 different ways the Lagrange interpolating polynomial for the following data:
x
f
(
x
) =
xe
x
x
0
= 0
0
x
1
= 1
e
x
2
= 2
2
e
2
Method 1:
by the definition of the Lagrange polynomial.
Method 2:
by Neville’s method.
Method 3:
by Newton’s interpolatory divideddifference formula.
II
For the data in problem I, write the error formula, and find an upper bound for the absolute
error, for
x
= 0
.
5.
III
1. Giving two points
x
0
and
x
0
+
h
, with
h >
0, and a function
f
∈
C
2
[
x
0
, x
0
+
h
], derive an
approximation to
f
′
(
x
0
), with error term.
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 Spring '08
 staff
 Math, Numerical Analysis, Characteristic polynomial, Diagonal matrix, Triangular matrix

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