An improved approach to automatic error cumulation control

Abstract

-For evahration of arithmetical expressions using multiple precision floating-point arithmetic, a method is given to automatically perform error cumulation control prior to the actual computations.Individual errors and their effects are identified, and it is shown how to compute these effects efficiently via automatic differentiation.In the presented approach these effects we used to determine which precisiorrs have to be chosen during the real computations, in order to limit error cumulation to admissible, user chosen error bounds.

Programming Environments for High Level Scientific Problem Solving. IFIP WG 2.5 Working Conference 6 Held in Karlsruhe, Germany on September 23 - 27, 1991

“…As a result of the first two necessary conditions, the module HSYM generates the three set of algebraic equations in dependence on the relation between a, and a 2 and under assumption that aCa 2 $ 0 in accordance with (1) Module ASYS allows readily to obtain all the solutions of (15)- (17). But construction of a symmetry according to algorithm of Sect.3 which are implemented in the module HSYM, may lead to new restrictions on the initial evolution equations in addition to those which follow from the necessary integrability conditions.…”

“…But then tools are required, as part of the symbolic-numeric interface, to determine a priori and automatically the precision required to perform these numerical computation in a reliable fashion. Work in this direction is also in progress [13,17]. A combined use of GENTRAN and SCOPE provides a simple mechanism for the construction of a fairly optimal description of MNV, as illustrated in Figure 2.…”

“…To our eyes. a control widget on-screen is like cliartjuink [17] in a line drawing: it may serve some valid purpose. but the overall effect is to distract from tile data.…”

On the Dimensional Estimate of Rounding-Errors of a typical Computing Process

“…To workup for the desired accuracy, numeric and symbolic techniques are combined in [15]. This approach is improved in [16], where they show how to use automatic differentiation to detect individual errors and there effects in a symbolicnumeric environment.…”