A New Approach to Error Arithmetic
Frank W. J. Olver · SIAM Journal on Numerical Analysis · 1978
By modification of the standard definition of relative error, a form of error arithmetic is developed that is well suited to floating-point computations. Rules are given for conversion from interval analysis to the new approach, and vice versa, both for real and complex variables. Illustrative applications include accumulation of products, quotients, sums and inner products, and the evaluation of polynomials. The paper also includes some new error bounds for basic operations in floating-point arithmetic.