EGN 4454 USF Quadratic Lagrange Interpolation and Nodal Values Problem Set

EGN 4454 Homework 4 Due Sunday, November 12th , 2023 11:59pm For all codes written, appropriate comments are required. Solutions must be uploaded in PDF format to Canvas. 1. Define the quadratic Lagrange interpolation functions for the following data points:[-2 -1 0 1 2 3.5 4 6 8]. Note that you will have to break up the interpolation into appropriate intervals for the number of points required to define the quadratic Lagrange functions. In other words, you cannot define Lagrange functions on all 9 data points at once. 2. Using your functions, interpolate the following nodal values [0.3784 -0.4546 0 0.4546 -0.3784 0.3285 0.4947 -0.2683 -0.1440] at x=[-1.5 .5 2 5 7]. You may use MATLAB to do this, but be sure you know how to do it by hand. For reference, a plot of the exact function, and the Lagrange interpolation of it are plotted below: 3. Use MATLAB’s polyfit and polyval functions to fit polynomials of degree 2, 4, 7 to the data in 1, and evaluate the approximating function at the selected points in Part 2. Plot your functions with the input data points and evaluated points shown. 1