Theory (60 points) 1. This is a table for our data set (x,y). (refer to page 8, 10, 14 on the lecture slide) X -1 0 0.5 1 y 2 1 0 1 a. (15 points) Find a linear interpolation function (1st order...

Please see instructions in the word document, you need to complete both theory and practice parts, submit solutions in a ipynb file.


Theory (60 points) 1. This is a table for our data set (x,y). (refer to page 8, 10, 14 on the lecture slide) X -1 0 0.5 1 y 2 1 0 1 a. (15 points) Find a linear interpolation function (1st order spline), L1, L2, L3. b. (15 points) Find a quadratic interpolation function (2nd order spline), Q1, Q2, Q3. c. (10 points) Find a Lagrange interpolation function. 2. (20 points) Determine the parameters a, b, c, d, and e so that S is a 3rd order cubic spline. (Refer to page 12 on the lecture slide) Practice (40 points) 1. (40 points/each 10 points) Using scipy.interpolate, please do interpolation for x=-1:0.01:1 with data set in the theory problem 1. (Refer to page 16, 27 on the lecture slide) a. Please do piecewise constant. Draw the plot. b. Please do linear interpolation. Draw the plot. c. Please do 3rd order spline. Draw the plot. d. Please do Radial basis function interpolation. Draw a plot.