A. Miller   M340   Mar 97  Computing Exercise

    %%%%%%% Worth 20 points - Due Friday Mar 21 %%%%%%%%%

   Matlab is available in the Computing Lab: Van Vleck 101 and many other
   computer labs across campus.  Matlab is a commercial program.  I have
   heard that a student version can be bought for about $150 in the Univ
   book store.

   Minimat is a "copy" of Matlab written by Joel Robbin (VV313). It is
   free.  I can give you the version for IBM pc compatibles if you bring
   me a disk or you can download it from:
     http://math.wisc.edu/~miller/ or http://math.wisc.edu/~robbin/
   There is also a version for the Macintosh on the homepages above.

   The Hilbert matrix H is defined by
      entry_{ij}(H)= 1/(i+j-1)
   where H is n x n.

   For n=3 H is:

      1   1/2   1/3
     1/2  1/3   1/4
     1/3  1/4   1/5

   The following .m file  will return the n-dimensional Hilbert matrix:
   %%%%%%%%%  HILBERT.M %%%%%%%%%%%%%%%%%%%%%%%%%%
      function H=hilbert(n)
         H=zeros(n,n);
         for i=1:n,
           for j=1:n,
             H(i,j)=1/(i+j-1);
           end
         end
   %%%%%%%%%  HILBERT.M %%%%%%%%%%%%%%%%%%%%%%%%%%

   The minimat-matlab commands needed are: inv, eye, det, max

   1.  turn on the diary file, e.g.  "diary myfile"
   2.  type "edit hilbert.m" and enter the above code and save it.
       (for matlab try "! edit hilbert.m" or "! vi hilbert.m")
   3.  for n=4 i.e. H  4 x 4: compute H
   4.  compute K the inverse of H
   5.  compute the maximum entry of K
   6.  compute the determinant of H and determinant of K and multiply together
   7.  multiply H by K and subtract the identity
   8.  compute L=H^2+7H
   9.  compute LH,  compute HL
   10. compute HL-LH
   11. compute 100000(HL-LH)
   12. repeat 4-11 for n=10 i.e. H 10 x 10
   13. save diary file using "diary off"
       (if you forgot to turn diary on, try "saveas opps")
   14. edit diary file removing junk you don't want me to see -
       add comments you do want me to see.
   15. Print out, read over, add comments in pencil or pen, hand in.