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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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
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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