In this question, you will construct the natural cubic spline, S for the following data. 1/4 1/2 3/4 1 -1 0 0 1 x f(x)
In this question, you will construct the natural cubic spline, S for the following data. 1/4 1/2 3/4 1 -1 0 0 1 x f(x)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.1: Systems Of Equations
Problem 15E
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Question
![4. In this question, you will construct the natural cubic spline, S for the following data.
1/4 1/2 3/4 1
-1 0 0 1
(a) Derive the system Ac = b to solve for the coefficients c; using the general formula.
The solution to each system is provided.
(1)
(2)
(3)
(4)
1/2 1/4
1/4 1 1/4
0 1/4
1
0
1
0 0
1/4 3/2 1/2 0
0 1/2 5/2 3/4
0
0
0
1
1
1/4
1/4
0 1/4 1/2
0 0
0
1 1/4 0
0 1/4 1 1/
0 0 0 1
X
f(x)
1/2
E---
C3
C1
-12
10-4
C4
7
C4
12
12
9
C3
C4
C1
232/15
C3
76/15
184/15
-92/15
-62/7
-27/14
0
48/5
48/5
0
1 1/4 1/16 1/64 C1
C2
198-8-8-4
1 3/4 9/16 27/64 C3
C4
9
1/3
−1/3](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F43db1c21-26d3-473a-8503-cd8e5f43a3f8%2F71f592eb-afee-4e4f-9da3-6ead6d80dd08%2Fcqtt9bc_processed.png&w=3840&q=75)
Transcribed Image Text:4. In this question, you will construct the natural cubic spline, S for the following data.
1/4 1/2 3/4 1
-1 0 0 1
(a) Derive the system Ac = b to solve for the coefficients c; using the general formula.
The solution to each system is provided.
(1)
(2)
(3)
(4)
1/2 1/4
1/4 1 1/4
0 1/4
1
0
1
0 0
1/4 3/2 1/2 0
0 1/2 5/2 3/4
0
0
0
1
1
1/4
1/4
0 1/4 1/2
0 0
0
1 1/4 0
0 1/4 1 1/
0 0 0 1
X
f(x)
1/2
E---
C3
C1
-12
10-4
C4
7
C4
12
12
9
C3
C4
C1
232/15
C3
76/15
184/15
-92/15
-62/7
-27/14
0
48/5
48/5
0
1 1/4 1/16 1/64 C1
C2
198-8-8-4
1 3/4 9/16 27/64 C3
C4
9
1/3
−1/3
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