Accession Number : ADA186614

Title :   Tensorial Calibration. 2. Second Order Tensorial Calibration.

Descriptive Note : Interim rept.,

Corporate Author : WASHINGTON UNIV SEATTLE LAB FOR CHEMOMETRICS

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

PDF Url : ADA186614

Report Date : 12 Oct 1987

Pagination or Media Count : 30

Abstract : Tensorial calibration provides a useful approach to calibration in general. For calibration of instruments that produce two dimensional (second order) data arrays of data per sample, tensorial concepts are a natural way of solving the calibration problems as vectorial concepts are for multivariate problems. Similarly, for third and higher order data, the tensorial description of calibration is also useful. This paper introduces second order calibration from a tensorial point of view. Univariate, multivariate and bilinear approaches to calibration are presented. The generalized rank annihilation method (GRAM) is described from the tensorial perspective, and it is shown that GRAM is equivalent to finding a second order tensorial base that spans both tensors (calibration and unknown) with respective diagonal component matrices. GRAM uses a single calibration sample of multicomponent analysis even in the presence of interferences. Second order bilinear calibration is extended to multiple calibration samples, where the effect of collinearities is reduced.

Descriptors :   *CALIBRATION, *TENSORS, *STATISTICAL ANALYSIS, ARRAYS, INSTRUMENTATION, MULTIVARIATE ANALYSIS, SAMPLING, VECTOR ANALYSIS, TWO DIMENSIONAL, CHEMICAL ANALYSIS

Subject Categories : Statistics and Probability
      Test Facilities, Equipment and Methods

Distribution Statement : APPROVED FOR PUBLIC RELEASE