Function name interpolate_spline

Input an array of x values, an array of y values

Outputa matrix with 3 columns and 1 rows where is the length of x (or produce an error if an issue is encountered)

Example

interpolate_spline([1,2,3], [2,6,8]) generates the matrix [2 6 -2; 6 2 0]

Hint 1 : You will need to solve a system of linear equations to get all the values. You do not need to program your own Gauss elimination to do this. Just use Matlabs linsolve command. Given a system of equations of the form = , you would use x =linsolve(A, b)

Hint 2 : The system of equations that appears in the spline equation only has non-zero values on 2 diagonal lines. You can use Matlabs diag command to help construct this matrix. Check the diag help page for more information

Hint 3 : It is possible to meet core requirements without any looping whatsoever. You can use loops if you want, but remember Matlabs array math.

Write a function that interpolates a set of data points using a quadratic spline and outputs a table of coefficients used for the spline fit (a in column 1, b in columns 2, c in column 3) Check to make sure that the same number of x and y data points have been provided (can be any number of data points) Given a set of (xi,y,) points, recall the quadratic spline fit process: 1. 2. Given n points, there should be n - 1 total spline polynomials aj is set to the value of f bi is solved from the following system of linear equations: 252-i 2(f3-f2) 2(f4-f3) 0 0 b2 0 0b3 1 1bn-2 2 3 2(fn-1-f-2) 1-2 fn-fn-1 11-1 Ci is solved from mh for [i = 1, n-2] 4. Cn-1 is set to 0 Write a function that interpolates a set of data points using a quadratic spline and outputs a table of coefficients used for the spline fit (a in column 1, b in columns 2, c in column 3) Check to make sure that the same number of x and y data points have been provided (can be any number of data points) Given a set of (xi,y,) points, recall the quadratic spline fit process: 1. 2. Given n points, there should be n - 1 total spline polynomials aj is set to the value of f bi is solved from the following system of linear equations: 252-i 2(f3-f2) 2(f4-f3) 0 0 b2 0 0b3 1 1bn-2 2 3 2(fn-1-f-2) 1-2 fn-fn-1 11-1 Ci is solved from mh for [i = 1, n-2] 4. Cn-1 is set to 0