1
COMPUTER SCIENCE 349A
Handout Number 20
EXAMPLES:
LAGRANGE INTERPOLATING POLYNOMIAL
1.
The case
n
=
1 is called linear interpolation, and consists of constructing a straight line
through 2 points
(
)
(
)
)
(
,
)
,
(
and
)
(
,
)
,
(
1
1
1
1
0
0
0
0
x
f
x
y
x
x
f
x
y
x
=
=
.
0
1
0
1
1
0
1
0
)
(
and
)
(
x
x
x
x
x
L
x
x
x
x
x
L
−
−
=
−
−
=
and thus
)
(
)
(
)
(
1
0
1
0
0
1
0
1
x
f
x
x
x
x
x
f
x
x
x
x
x
P
−
−
+
−
−
=
.
Note that
P
(
x
)
is clearly a linear (first order) polynomial in the variable
x
, and that
)
(
)
(
and
)
(
)
(
1
1
0
0
x
f
x
P
x
f
x
P
=
=
,
which verifies that
P
(
x
)
is the desired interpolating polynomial.
2.
A complete elliptic integral is defined by
∫
−
=
2
/
0
2
2
sin
1
)
(
π
z
k
dz
k
K
.
The following values can be obtained from numerical tables:
sin
−
1
k
K
(
k
)
65
o
2.3088
66
o
2.3439
67
o
2.3809
Construct the quadratic (order

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