An Interval Algorithm for Solving Systems of Linear Equations to
James Weldon Demmel, Fritz Krückeberg · 1983
We describe an interval arithmetic algorithm for solving a special class of simultaneous linear equations. This class includes but is not limited to systems Ax=b where a and b have integer entries. The algorithm uses fixed point arithmetic, and has two properties which distinguish it from earlier algorithms: given the absolute accuracy e desired, the algorithm uses only as much precision as needed to achieve it, and the algorithm can adjust its own parameters to minimize computation time.