A Schur complement approach for computing subcovariance matrices arising in a road safety measure modelling

Authors:
Assi N'Guessan;Claude Langrand
Affiliations:
Ecole Polytechnique Universitaire de Lille et Laboratoire de Mathématiques Appliquées CNRS, FRE 2222, Université de Lille 1 and Dept. of Stat. and Comp. Sci., Bât. Polytech'Lil ...;Laboratoire de Mathématiques Appliquées CNRS, FRE 2222.- U.F.R. de Mathématiques pures et appliquées, Université de Lille 1, 59655 Villeneuve d'Ascq, Cedex, France
Venue:
Journal of Computational and Applied Mathematics
Year:
2005

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Abstract

This paper deals with the determination of the analytical expression of a real partitioned matrix inverse. A formal inversion method is suggested through Schur complements and the elements of any inverse matrix block are explained, irrespective of the size of the considered matrix. The suggested approach does not need any matrix inversion numerical program. This methodology is applied to a Fisher information matrix relating to a multidimensional modelling of road accident data when a road safety measure is applied on different experiment sites. An example of formal calculation and interpretation is given to support our approach.