Optimal Signed Relative Error for Floating-Point Arithmetic

Abstract

Abstract. Floating-point number and its arithmetic are widely used in numerical computations. Because information of the floating-point numbers is finite, a rounding error may occur in floating-point arithmetic. The optimal relative error bound for floating-point arithmetic is given by Jeannerod and Rump. In this paper, we extend the discussion to signed relative error and derive the optimal range of the signed relative error.