Computer Science 6676, Spring 1999                                         February 5, 1999

Assignment 2

Due Wednesday, February 17    (at beginning of class)


  1. Chapter 3, problems 9, 17.
  1. 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.
  1. 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.)
  1. 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.)