Topics in Comptuter Algebra: V

Introduction to computational linear algebra.

Michael Monagan, Department of Mathematics, Simon Fraser University.

Wednesday July 15, 2009, K9509, 3:30-5:00pm.

Let A be an n by n matrix of integers and b be a vector of n integers.
Two fundamental operations are the computation of det(A) and solving the
linear system Ax=b for x in Q^n.  Here we are interested in exact algorithms.
We will present the Bareiss (Edmonds) fraction-free algorithm for computing
det(A) and compare it with using Chinese remaindering.
To solve Ax=b we will study the Moeck-Carter p-adic algorithm which
uses Wang's rational reconstruction algorithm.