Rounding Error Analysis of Interval Algorithms
Friedrich Stummel · ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik · 1984
Abstract Using the linearization method, a rounding error analysis of interval algorithms is established. It is shown that the interval midpoints and radii are approximate solutions of real evaluation algorithms and of certain linear systems uniquely associated to each interval algorithm. In addition, interval data and interval rounding condition numbers are defined which yield optimal bounds of the possible magnitude of the interval radii. These concepts and tools are applied to the following numerical examples: evaluation of a polynomial, continued fraction expansion, summation procedure, and Cramer's rule for two linear equations in two unknowns.