Description This assignment will cover chapters 3 and 4 . Heads up, this require tons of programming. During chapters 3 and 4 , we will be covering interpolating polynomials. Polynomial interpolation is the interpolation of a given data set by the polynomial of lowest possible degree that passes through the points of the dataset. This can help us by approximating points on complicated curves. However, this requires tons of operations on different points along the curve and introduces matrix operations. Please do not procrastinate and get a head start on this assignment. For full credit on this assignment, the following is required: - Create expected structure - ensure there's a readme with instructions on how to compile - every output for each question is correct Constraints Standard Structure For this assignment, you will need the following structure: Top Level Please ensure your repository is named "cot-4500-as2". Compilation Instructions Keeping true to adding industry likeness to each assignment, it is required that you need to include a README per repository. A README is a file used to describe a repo's purpose, include compilation purposes, or both. A proper README.md is typically filled out with sections, akin to an essay. For this assignment, a README needs to be included and filled out. The amount of info you put into the README is up to you, but you will need the following at least: - Mention of requirements.txt - No need to include this UNLESS you plan on using a library other than NumPy - Mention of running python Since we require instructions on to run, you will need to include the command to run the script from command line. Questions 1. Using Neville's method, find the 2 ad degree interpolating value for f(3.7) for the following set of data a. 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. 3. Using the results from 3 , approximate f(7.3) ? 4. Using the divided difference method, print out the Hermite polynomial approximation matrix 5. Using cubic spline interpolation, solve for the following using this set of data: a. Find matrix A b. Vector b c. Vector x Description This assignment will cover chapters 3 and 4 . Heads up, this require tons of programming. During chapters 3 and 4 , we will be covering interpolating polynomials. Polynomial interpolation is the interpolation of a given data set by the polynomial of lowest possible degree that passes through the points of the dataset. This can help us by approximating points on complicated curves. However, this requires tons of operations on different points along the curve and introduces matrix operations. Please do not procrastinate and get a head start on this assignment. For full credit on this assignment, the following is required: - Create expected structure - ensure there's a readme with instructions on how to compile - every output for each question is correct Constraints Standard Structure For this assignment, you will need the following structure: Top Level Please ensure your repository is named "cot-4500-as2". Compilation Instructions Keeping true to adding industry likeness to each assignment, it is required that you need to include a README per repository. A README is a file used to describe a repo's purpose, include compilation purposes, or both. A proper README.md is typically filled out with sections, akin to an essay. For this assignment, a README needs to be included and filled out. The amount of info you put into the README is up to you, but you will need the following at least: - Mention of requirements.txt - No need to include this UNLESS you plan on using a library other than NumPy - Mention of running python Since we require instructions on to run, you will need to include the command to run the script from command line. Questions 1. Using Neville's method, find the 2 ad degree interpolating value for f(3.7) for the following set of data a. 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. 3. Using the results from 3 , approximate f(7.3) ? 4. Using the divided difference method, print out the Hermite polynomial approximation matrix 5. Using cubic spline interpolation, solve for the following using this set of data: a. Find matrix A b. Vector b c. Vector x