Computer Science 6676, Spring 1999
February 5, 1999
Assignment 2
Due Wednesday, February 17 (at beginning of class)
Chapter 3, problems 9, 17.
Derive a row-oriented Cholesky factorization, ie one that computes
the values of L one row at a time (rather than one column
at a time as given in class). Give the pseudo-code for your algorithm,
and confirm that it works correctly on problem 17 above.
Prove that if an n x n real matrix A has a factorization
A = L x (L^T), where L is non-singular, then A
is symmetric and positive definite. (Hint: you should be able to do this
in a few lines.)
Chapter 4, problems 15, 16. (For problem 16, you don't have to deal
with the case where A does not have full column rank, but it is
a nice challenge to try to handle this case.)