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Generalized numerical error analysis with applications to geochronology and thermodynamics
Institution:1. Istituto per Applicazioni del Calcolo M. Picone, via Amendola 122/D, 70126 Bari, Italy;2. Istituto di Metodologie Organiche e dei Plasmi, via Amendola 122/D, 70126 Bari, Italy;1. State Key Laboratory of Earthquake Dynamics, Institute of Geology, China Earthquake Administration, Yard No.1, Hua Yan Li, Chaoyang District, Beijing, 100029, PR China;2. State Key Laboratory of Lithospheric Evolution, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, 100029, PR China;3. Physical Institute, Space Sciences and Planetology, University of Bern, Bern, Switzerland;4. Key Laboratory of Planetary Geological Evolution and Institute of Meteorites and Planetary Materials Research, Guilin University of Technology, Guilin, 541004, PR China;5. State Key Laboratory of Isotope Geochemistry, Guangzhou Institute of Geochemistry, Chinese Academy of Sciences, Guangzhou, 510640, PR China;1. Department of Mathematics, School of Science and Technology, Meiji University, 1-1-1 Higashi-mita, Tama-ku, Kawasaki 214-8571, Japan;3. Institute of Mathematics, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet Road, 10307 Hanoi, Viet Nam;4. Mathematik und Informatik, Universität des Saarlandes, Campus E2 4, D-66123 Saarbrücken, Germany
Abstract:A general numerical error propagation procedure is developed to calculate the error in a quantity derived from measurements which are subject to errors. It is an alternative to computer intensive techniques such as Monte Carlo and can be applied to quite complex analytical problems where correlation among the measurement errors and among the final errors in results are present. Previous formulations have usually ignored correlated errors. Some of the assumptions involved in error propagation can also be checked numerically. This is an advantage over analytical formulations which cannot assess the validity of the calculated errors. Formulation as computer subroutines permits the analysis to be added to existing programs. Examples from the fields of geochronology and thermodynamics are used to highlight the advantages and the flexibility of the method.
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