An Alternative Approach for Solving Ill-conditioned Systems of Linear Equations

Abstract

The techniques directed toward errors containment for solving ill-conditioned linear systems Ax=b, is an important topic in both applied mathematics and computer science. Usually floating point numbers are used to represent real numbers, and any computation involving floating point is subject to several types of errors (inherent errors, truncation errors, and round-off errors). These errors are usually accepted. But in critical situations it is considered a catastrophic. The aim of this paper is to provide an alternative approach for solving ill-conditioned linear systems using rational numbers with long integer capacities, and demonstrate this by empirical tests of various known illconditioned cases. The results indicate computing with rational numbers does not suffer from round-off errors accumulation.