7. Find the parameters a, b, c so that the following function is a cubic spline: 1 8+ ax + 4x? 3 on [0, 1] 8. (x – 1) + b(x – 1)² – ;(x – 1)³ 1 S(x) = {2 on [1, 2] %3D | 3 1 2+ c(x – 2) +2(x – 2)2 3 (x – 2)³ on [2, 3] | Which of the three conditions (natural, parabolically terminated, or not-a-knot), if any, are satisfied?
7. Find the parameters a, b, c so that the following function is a cubic spline: 1 8+ ax + 4x? 3 on [0, 1] 8. (x – 1) + b(x – 1)² – ;(x – 1)³ 1 S(x) = {2 on [1, 2] %3D | 3 1 2+ c(x – 2) +2(x – 2)2 3 (x – 2)³ on [2, 3] | Which of the three conditions (natural, parabolically terminated, or not-a-knot), if any, are satisfied?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![7. Find the parameters a, b, c so that the following function is a cubic spline:
1
8+ ax + 4?
3
on [0, 1]
8
1
S(x) = {2 -
(x – 1) + b(x – 1)²
(r – 1) on [1,2]
on [1, 2]
3
3
1
2+ c(x – 2) + 2(x – 2)² – (x – 2)³
3
on [2, 3]
Which of the three conditions (natural, parabolically terminated, or not-a-knot),
if any, are satisfied?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3e085104-fb6a-40f0-89db-c0353a727e3b%2Fc34dff15-05f4-42da-843c-624fb6a0328d%2Fcz9macw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:7. Find the parameters a, b, c so that the following function is a cubic spline:
1
8+ ax + 4?
3
on [0, 1]
8
1
S(x) = {2 -
(x – 1) + b(x – 1)²
(r – 1) on [1,2]
on [1, 2]
3
3
1
2+ c(x – 2) + 2(x – 2)² – (x – 2)³
3
on [2, 3]
Which of the three conditions (natural, parabolically terminated, or not-a-knot),
if any, are satisfied?
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