Accession Number : ADA186708

Title :   Tensorial Calibration. 1. First Order Tensorial Calibration.

Descriptive Note : Interim rept.,

Corporate Author : WASHINGTON UNIV SEATTLE LAB FOR CHEMOMETRICS

Personal Author(s) : Sanchez, Eugenio ; Kowalski, Bruce R.

Report Date : 12 OCT 1987

Pagination or Media Count : 43

Abstract : Many analytical instruments now produce one-, two- or n-dimensional arrays of data that must be used for the analysis of samples. An integrated approach to linear calibration of such instruments is presented from a tensorial point of view. The data produced by these instruments is seen as the components of a first, second or the order tensor, respectively. In this first paper, concepts of linear multivariate calibration are developed in the framework of first order tensors, and it is shown that the problem of calibration is equivalent to finding the contravariant vector corresponding to the analyte being calibrated. A model of the subspace spanned by the variance in the calibration must be built to compute the contravariant vectors. It is shown that the only difference between methods such as least squares, principal components regression, ridge regression, latent root regression and partial least squares resides in the choice of the model.

Descriptors :   *CALIBRATION, *MULTIVARIATE ANALYSIS, *TENSOR ANALYSIS, REGRESSION ANALYSIS, DORMANCY, LINEAR SYSTEMS, TENSORS, LEAST SQUARES METHOD, RIDGES, INSTRUMENTATION, LABORATORY PROCEDURES.

Subject Categories : Test Facilities, Equipment and Methods
      Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE