Topics in Comptuter Algebra: V
Introduction to computational linear algebra.
Michael Monagan, Department of Mathematics, Simon Fraser University.
Abstract: 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.