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Problem 3: (23 pts) Consider the following table: X 1 1.1 1.2 1.3 1.4 cos(x) 0.54030 0.45360 0.36236 0.26750 0.16997 (i) [10 points] Using Newton Interpolation, write a program to obtain (ii) [2 points] A polynomial of degree 1 that interpolates $cos(x)$. (iii) [2 points] A polynomial of degree 2 that interpolates $cos(x)$. (iv) [2 points] A polynomial of degree 3 that interpolates $cos(x)$. (v) [2 points] A polynomial of degree 4 that interpolates $cos(x)$. (vi) [5 points] Compute $cos(1.05)$ using the various order polynomials and investigate the error for the Newton polynomial approximations in (ii) - (v)

          Problem 3: (23 pts) Consider the following table:
X
1
1.1
1.2
1.3
1.4
cos(x) 0.54030 0.45360 0.36236 0.26750 0.16997
(i) [10 points] Using Newton Interpolation, write a program to obtain
(ii) [2 points] A polynomial of degree 1 that interpolates $cos(x)$.
(iii) [2 points] A polynomial of degree 2 that interpolates $cos(x)$.
(iv) [2 points] A polynomial of degree 3 that interpolates $cos(x)$.
(v) [2 points] A polynomial of degree 4 that interpolates $cos(x)$.
(vi) [5 points] Compute $cos(1.05)$ using the various order polynomials and investigate the error for the Newton polynomial approximations in (ii) - (v)

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Problem 3: (23 pts) Consider the following table:
X
1
1.1
1.2
1.3
1.4
cos(x) 0.54030 0.45360 0.36236 0.26750 0.16997
(i) [10 points] Using Newton Interpolation, write a program to obtain
(ii) [2 points] A polynomial of degree 1 that interpolates cos(x).
(iii) [2 points] A polynomial of degree 2 that interpolates cos(x).
(iv) [2 points] A polynomial of degree 3 that interpolates cos(x).
(v) [2 points] A polynomial of degree 4 that interpolates cos(x).
(vi) [5 points] Compute cos(1.05) using the various order polynomials and investigate the error for the Newton polynomial approximations in (ii) - (v)

Added by Heather P.

Computer Science and Information Technology

Trishna Knowledge Systems 2018 Edition

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Solved by Expert Liliane Martins

Step 1

The divided differences can be calculated using the following formula: f[x0] = f(x0) f[x0, x1] = (f[x1] - f[x0]) / (x1 - x0) f[x0, x1, x2] = (f[x1, x2] - f[x0, x1]) / (x2 - x0) f[x0, x1, x2, x3] = (f[x1, x2, x3] - f[x0, x1, x2]) / (x3 - x0) f[x0, x1, x2, x3, x4] Show more…

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Using Python Please Problem 3: (23 pts) Consider the following table: x 1 1.1 1.2 1.3 1.4 cos(x) 0.54030 0.45360 0.36236 0.26750 0.16997 (i [10 points] Using Newton Interpolation, write a program to obtain (ii) [2 points] A polynomial of degree 1 that interpolates cos(x). (iii) [2 points] A polynomial of degree 2 that interpolates cos(x) (iv) [2 points] A polynomial of degree 3 that interpolates cos(x) (v) [2 points] A polynomial of degree 4 that interpolates cos(x). (vi) [5 points] Compute cos(1.05) using the various order polynomials and investigate the error for the Newton polynomial approximations in (ii) - (v)

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