Math 543 Computer Project 02

For this project you will need to use a mathematics software tool package like Matlab, Maple or Mathematica, or a programming language. The project will involve the use of the four test functions
  1. Construct a procedure or function that will determine the coefficients for the cubic B-spline respresentation for the clamped (or complete) interpolating spline S(x) for a set of equally spaced data values. The procedure should have as input parameters: The output should be an array of length m+2 of cubic B-spline coefficients.
  2. Construct a procedure or function that will evaluate the B-spline representation for a clamped (or complete) interpolating cubic spline S(x) at a particular point xp. The procedure should have as input parameters: The output should be the value of the spline at xp.
  3. Construct a procedure or function that will compute the integral of the the B-spline representation for a clamped (or complete) interpolating cubic spline S(x) over the interval of definition [a,b] for the original function f(x) which S(x) interpolates. The procedure should have as input parameters: The output should be the value of the integral of the spline.
  4. For each of the four functions determine coefficients for the spline S(x) for m = 5, 9, 17 and 33, and
  5. Hand in your computer source code, graphs, and a brief discussion of your results. Make sure that your source code is well-structured and reasonably efficient, with some comments to explain what you have done.