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A function S is defined on the interval [-1,3] by S₁(x), xЄ[-1,0), S(x) = S2(x), xЄ [0,2), S3(r), x € [2,3, where S1, S2 and S3 are cubic polynomials. Write down the system of twelve equations that must be satisfied if S is a natural cubic spline interpolating the function defined by equations f(x1)=-3, f(x2) = 1 f(x3) = -3 and f(x4) = (5)

A function S is defined on the interval [-1,3] by S₁(x), xЄ[-1,0), S(x) = S2(x), xЄ [0,2), S3(r), x € [2,3, where S1, S2 and S3 are cubic polynomials. Write down the system of twelve equations that must be satisfied if S is a natural cubic spline interpolating the function defined by equations f(x1)=-3, f(x2) = 1 f(x3) = -3 and f(x4) = (5)

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 70EQ
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A function S is defined on the interval [-1,3] by S₁(x), x = [−1,0), S(x) S2(x), x = [0,2), S3(x), x = [2,3], where S1, S2 and S3 are cubic polynomials. Write down the system of twelve equations that must be satisfied if S is a natural cubic spline interpolating the function defined by equations f(x1)=-3, f(x2) = 1 f(x3) = -3 and f(x4) = 1, (5)
Transcribed Image Text:A function S is defined on the interval [-1,3] by S₁(x), x = [−1,0), S(x) S2(x), x = [0,2), S3(x), x = [2,3], where S1, S2 and S3 are cubic polynomials. Write down the system of twelve equations that must be satisfied if S is a natural cubic spline interpolating the function defined by equations f(x1)=-3, f(x2) = 1 f(x3) = -3 and f(x4) = 1, (5)
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