Increasing the Reliability of Numerical Data Using Several Methods Under Conditions of Indeterminacy

Abstract

In order to increase data reliability, between two and four methods may be used to solve the same problem, with the results being compared. An estimation of the error in every method must be found. The paper offers a mathematical model for the unobservable component of the error, which may be caused by various factors (for example, software implementation). This gives a numerical characteristic of certainty. The main assumption is that the errors from the different methods may be considered as independent random quantities. Moreover, the probability density of the error has a single maximum at zero. In connection with the indeterminacy of the probability densities, the worst case distribution functions (leading to maximum error probability) must be found. An estimate is obtained of the probability of the existence of an error greater than some given value, under the condition that the results coincide up to the accuracy of the computations. Keywords—programmer mistake, undetermined error, computer methods, indeterminacy intervals comparison