Homework 1 Foundations of Computational Math 2 Spring
2011
Solutions will be posted Monday, 1/17/11
Written homework problems are study questions. You need not turn in solutions but you
are strongly encouraged to do the problems and read the posted solutions carefully.
Problem 1.1
Consider the data points
(
x,y
) =
{
(0
,
2)
,
(0
.
5
,
5)
,
(1
,
8)
}
Write the interpolating polynomial in both Lagrange and Newton form for the given
data.
Problem 1.2
Use this divided difference table for this problem. Justify all of your answers.
i
0
1
2
3
4
5
x
i
−
1
0
2
4
5
6
f
i
13
2
−
14
18
67
91
f
[
−
,
−
]
−
11
−
8
16
49
24
f
[
−
,
−
,
−
]
1
6
11
−
25
/
2
f
[
−
,
−
,
−
,
−
]
1
1
−
47
/
8
f
[
−
,
−
,
−
,
−
,
−
]
0
−
55
/
48
f
[
−
,
−
,
−
,
−
,
−
,
−
]
−
55
/
336
1.2.a
Use the divided difference information about the unknown function
f
(
x
) and consider the
unique polynomial, denoted
p
1
,
5
(
x
), that interpolates the data given by pairs (
x
1
,f
1
), (
x
2
,f
2
),
(
x
3
,f
3
), (
x
4
,f
4
) , and (
x
5
,f
5
). Use two different sets of divided differences to express
p
1
,
5
(
x
)
in two distinct forms.