An interval algorithm for solving systems of linear equations to prespecified accuracy (Q760758)

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 \(\epsilon\) 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.