A Relation Between Morphological and Interval OperationsSpringer Science and Business Media LLC - Tập 4 - Trang 167-178 - 1998
Antony T. Popov
In our work we show that the operations of interval algebra can be expressed by morphological operations on an appropriately chosen lattice defined over the set of intervals on the real line, when regarding real interval arithmetic, and in the complex plane, when regarding complex interval arithmetic. Using the morphological representation of the interval operations, a generalization of the additi...... hiện toàn bộ
On Overestimations Produced by the Interval Gaussian AlgorithmSpringer Science and Business Media LLC - Tập 3 - Trang 363-368 - 1997
Jiří Rohn
Interval Gaussian algorithm is a popular method for enclosing solutions of linear interval equations. In this note we show that both versions of the method (with or without preconditioning) may yield large overestimations for arbitrarily small data widths even in case n = 4.
Rump's Example RevisitedSpringer Science and Business Media LLC - Tập 8 - Trang 245-248 - 2002
Eugene Loh, G. William Walster
Rump published an example (Algorithms for Verified Inclusions: Theory and Practice, in: Moore, R. E. (ed.), Reliability in Computing: The Role of Interval Methods in Scientific Computing, Academic Press, Boston, 1988, pp. 109–126) in which numerical evaluation of an expression gave a misleading result, even though use of increasing arithmetic precision suggested reliable computation. This oft-cite...... hiện toàn bộ
Interval Monte Carlo as an Alternative to Second-Order Sampling for Estimating Ecological RiskSpringer Science and Business Media LLC - Tập 13 - Trang 71-81 - 2006
Janos G. Hajagos
Interval Monte Carlo offers an alternative to second-order approaches for modeling measurement uncertainty in a simulation framework. Using the example of computing quasi-extinction decline risk for an ecological population, an interval Monte Carlo model is built. If the model is not written optimally, the mean and standard deviation of the growth rate repeat, then the bounds on the quasi-extincti...... hiện toàn bộ
PrefaceSpringer Science and Business Media LLC - Tập 2 - Trang i-i - 1996
Günther Mayer, Vladik Kreinovich
Verified Error Bounds for Linear Systems Through the Lanczos ProcessSpringer Science and Business Media LLC - Tập 5 - Trang 255-267 - 1999
Andreas Frommer, Andre Weinberg
We use verified computations and the Lanczos process to obtain guaranteed lower and upper bounds on the 2-norm and the energy-norm error of an approximate solution to a symmetric positive definite linear system. The upper bounds require the a priori knowledge of a lower bound on the smallest eigenvalue.