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4. Using the divided difference method, print out the Hermite polynomial approximation matrix X 3.6 3.8 3.9 f(x) 1.675 1.436 1.318 f(x) -1.195 -1.188 -1.182

4. Using the divided difference method, print out the Hermite polynomial approximation matrix X 3.6 3.8 3.9 f(x) 1.675 1.436 1.318 f(x) -1.195 -1.188 -1.182

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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Please solve this in Python! Second picture is the expected output. 

[[ 3.6 [ 3.6 [ 3.8 [ 3.8 [ 3.9 [ 3.9 1.675 1.675 1.436 1.436 1.318 1.318 0. -1.195 -1.195 -1.188 -1.18 -1.182 0. 0. -0. 0.035 0.08 -0.02 0. 0. 0.175 0.15 -1. 0. 0. ] ] -0.0833333] -3.8333333]]
Transcribed Image Text:[[ 3.6 [ 3.6 [ 3.8 [ 3.8 [ 3.9 [ 3.9 1.675 1.675 1.436 1.436 1.318 1.318 0. -1.195 -1.195 -1.188 -1.18 -1.182 0. 0. -0. 0.035 0.08 -0.02 0. 0. 0.175 0.15 -1. 0. 0. ] ] -0.0833333] -3.8333333]]
4. Using the divided difference method, print out the Hermite polynomial approximation matrix X 3.6 3.8 3.9 f(x) 1.675 1.436 1.318 f'(x) -1.195 -1.188 -1.182
Transcribed Image Text:4. Using the divided difference method, print out the Hermite polynomial approximation matrix X 3.6 3.8 3.9 f(x) 1.675 1.436 1.318 f'(x) -1.195 -1.188 -1.182
Expert Solution
Step 1

Algorithm:

1. Create an array to store the values of X, f(x), and f'(x).

2. Initialize an array to store the coefficients of the Hermite polynomial.

3. For each value of X, calculate the coefficient of the corresponding Hermite polynomial.

4. If i = 0, set the coefficient to f(x).

5. If i = 1, set the coefficient to (f(x1) – f(x0))/(x1 – x0).

6. If i > 1, set the coefficient to (coeffs(i-1)-coeffs(i-2))/(x(i) – x(i-2)).

7. Print the Hermite polynomial approximation matrix and the coefficients of the Hermite polynomial.

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