Please help me solve this using python. Add the code used to solve it. The expected output is Question 2:[9.210500000000001, 17.00166666666675, -141.82916666666722]Question 3:24.016574999999992 2. Using Newton's forward method, print out the polynomial approximations for degrees 1, 2,and 3 using the following set of dataa. Hint, create the table firstb.X7.27.47.57.63. Using the results from 3, approximate f(7.3)?f(x)23.549225.391326.822427.4589

The algorithm for code 1 can be described as follows: Initialize the coefficients list and append…

Answered: 2. Using Newton's forward method, print…

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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Question

Please help me solve this using python. Add the code used to solve it.

The expected output is

Question 2:

[9.210500000000001, 17.00166666666675, -141.82916666666722]

Question 3:
24.016574999999992

2. Using Newton's forward method, print out the polynomial approximations for degrees 1, 2,
and 3 using the following set of data
a. Hint, create the table first
b.
X
7.2
7.4
7.5
7.6
3. Using the results from 3, approximate f(7.3)?
f(x)
23.5492
25.3913
26.8224
27.4589

Expert Solution

Step 1

The algorithm for code 1 can be described as follows:

Initialize the coefficients list and append the first y value to it.
Loop through the range of 1 to the length of the x values (len(x)).
In the inner loop, go through the range of len(x) - 1 down to the current j value minus 1 (j-1) in decrements of -1.
Calculate the current coefficient by subtracting the previous coefficient (coefficients[i-1]) from the current coefficient (coefficients[i]) and dividing the result by the difference between the current x value (x[i]) and the previous x value (x[i-j]).
Update the current coefficient in the coefficients list with the calculated value.
Repeat steps 3-5 until all coefficients have been calculated and stored in the coefficients list.
Print the final coefficients list, which contains the calculated coefficients of the polynomial approximation of the function represented by the data points.

The algorithm for code 2 can be described as follows:

Define the x and y data points.
Initialize an empty list to store the coefficients.
Loop through the x data points and append the corresponding y value to the coefficients list.
Nested loop to calculate the coefficients using Newton's Forward Method formula: a. The outer loop ranges from 1 to the length of x. b. The inner loop ranges from the length of x to the value of the outer loop variable minus 1, decrementing by 1. c. For each iteration of the inner loop, calculate the coefficient using the formula: coefficients[i] = (coefficients[i]-coefficients[i-1])/(x[i]-x[i-j])
Initialize a variable to store the result.
Loop through the coefficients list, multiply each coefficient with the product of (7.3 - x[j]) for all j less than i, and add the result to the result variable.
Print the result.

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Follow-up Question

How do I omit "23.5492" from the ouput of the first code? It is supposed to print out [9.210500000000001, 17.00166666666675, -141.82916666666722]

but it is printing:

[23.5492, 9.210500000000001, 17.00166666666675, -141.82916666666722]

Solution

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