Systematic Search for Orthogonal Systems in the Calibrations of Submultiples and Multiples of the Unit of Mass
Year: 1980
Type: article
Abstract: The structure of the design matrix of a system of equations of condition which are formed in taking the observations for calibration of a "series of mass standards", has a strong influence on the accuracy of the results. It was suggested by Prowse and Anderson (1974) that the best system of equations, both from the standpoint of the ease of numerical calculations and the magnitude of the standard deviations on individual components, is that in which the design matrix is orthogonal. Grabe (1978), by introducing the principle that some of the possible equations may be omitted and some repeated, produced a system in the series 10, 5, 3, 2, 1, 1', the design matrix of which is orthogonal. The present article describes an original method which conforms to Grabe's principles and leads to systems of equations which possess orthogonal matrices and which can be easily applied to various "series of mass standards" used in practical metrology.
Source: Metrologia
Authors: M Zuker, G Mihailov, M Romanowski
Institutions: National Research Council Canada, Government of Canada
Language: English
Subfield: Statistics, Probability and Uncertainty
Field: Decision Sciences
Domain: Social Sciences
Open Access status: bronze
OpenAlex ID: W2077181092