Homework 2 
                          MA/CS 375, Spring 2002
                             Due Friday March 1 

This homework will count as part of your grade so you must work independently.
It is permissible to discuss it with your instructor, fellow students,
and friends. However, the programs/scripts and report must be done only
by the student doing the project. TURN IN TESTS OF ALL FUNCTIONS YOU WRITE!
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[i.] Write a function which computes the infinity norm condition
number of an nXn matrix, using the built-in Matlab function
inv. Using the Matlab function randn, generate a reasonable sample
of random matrices and compute their condition numbers. Plot the mean
of the condition numbers for n=10,20,40,80. How does the mean
condition number scale with n?
[ii.] 5.2.7 (Record the flops required as a function of n and
k for the examples you choose.)
     MatPower-------bin
[iii.] 5.2.12 (Record the flops required as a function of n 
for the examples you choose.)
     Triu-Trid
[iv.] 5.4.2  
     CSinterp, CSeval, FFTrecur
     f(1:2*m=n)
     y = (2/n)F_n f = a* - i b* (real n-vectors)
***  a_j = { a*_j/2;j=(1,m+1) , a*_j;j=2:m }    ----> F.a
     b_j = b*_{j+1};j=1:m-1                     ----> F.b    
   Replace CS eval with a call to FFTrecur
[v.] 6.1.5
     TriuInv: invert an upper-triangular matrix