A study of Auchmutyʹs error estimate

We analyze the absolute error estimate of Auchmuty [1] developed for linear systems. In the Euclidean norm, this estimate and its geometrical interpretation are derived from the Kantorovich inequality. The estimate is then compared with other estimates known in the literature. A probabilistic analysis and extension of the estimate to nonlinear systems are also given. We also report on computational test results, which indicate that Auchmutyʹs estimate is an appropriate tool for practice.