A natural cubic spline S on [0, 2] is defined by: so(x) = 1+2x– x³ 0≤x≤1 S(x) = { $₁(x) $₁(x) = 2 + b(x - 1) + c(x − 1)² + d(x -1)³ 1≤x≤2 Find b, c, and d. Note: You could utilize code or write this as a linear system, but since this is only two splines, you might find it easier to just work with the standard conditions of matching at data points and continuity to determine coefficients.
A natural cubic spline S on [0, 2] is defined by: so(x) = 1+2x– x³ 0≤x≤1 S(x) = { $₁(x) $₁(x) = 2 + b(x - 1) + c(x − 1)² + d(x -1)³ 1≤x≤2 Find b, c, and d. Note: You could utilize code or write this as a linear system, but since this is only two splines, you might find it easier to just work with the standard conditions of matching at data points and continuity to determine coefficients.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.5: Systems Of Linear Equations In More Than Two Variables
Problem 44E
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![A natural cubic spline S on [0, 2] is defined by:
= 1+2x– x³
0<x< 1
S(x) = { $₁(x) = 2 + 6(x²-1) ++ (x −1)²+d(x-1)³ 1≤x≤2
Find b, c, and d.
Note: You could utilize code or write this as a linear system, but since this is only two splines, you
might find it easier to just work with the standard conditions of matching at data points and continuity
to determine coefficients.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd8694f02-79fe-4b76-9079-b1456b2e1bd2%2F94602a4f-ad6b-4d4b-94f6-bf9a786f4af1%2F9w2tqyr_processed.png&w=3840&q=75)
Transcribed Image Text:A natural cubic spline S on [0, 2] is defined by:
= 1+2x– x³
0<x< 1
S(x) = { $₁(x) = 2 + 6(x²-1) ++ (x −1)²+d(x-1)³ 1≤x≤2
Find b, c, and d.
Note: You could utilize code or write this as a linear system, but since this is only two splines, you
might find it easier to just work with the standard conditions of matching at data points and continuity
to determine coefficients.
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