Homework 2, due October 13:

This time most of them are from Van Loan's book. Explain your answers and try to relate the output from your runs to material covered in the text book and in class.
  1. P1.4.5 on p. 47
  2. P1.4.6 on p. 47
  3. P1.4.8 on p. 48
  4. P1.4.10 on p. 48
  5. P1.5.6 on p. 59
    1. Download RungeEg.m, and the other m-files required when RungeEg.m is run, e.g., from the Cornell web site , or from my homepage.
    2. Revise it by adding a facility that prints a table of the largest error as a function of the degree of the interpolation polynomial. Also print the value of x where the maximum of the absolute value of the error occurs.
    3. Change the points, where we interpolate, to

      Note that we have points at both end points of the interval and that the points generally now are much more crowded towards the ends where the error was quite bad before. Compute the maximum interpolation error over the interval [-1,+1]. Print the error curve for four selected values on n, preferably on one sheet of paper.
    4. Try the same two sets of points for a function of your own choice.

Homework should be given in hard copy to me in class or in my office, or left under my office door, or given directly to the grader, goldfelp@cims.nyu.edu in room 808, Warren Weaver Hall.

Please do not leave homework in my lobby mailbox.

Homework is due at midnight on the due date. Late homework will be penalized 20%, and will NOT be accepted after November 1.