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An improved algorithm for the generalized rank annihilation method
Author(s) -
Wilson Bruce E.,
Sanchez Eugenio,
Kowalski Bruce R.
Publication year - 1989
Publication title -
journal of chemometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.47
H-Index - 92
eISSN - 1099-128X
pISSN - 0886-9383
DOI - 10.1002/cem.1180030306
Subject(s) - orthonormal basis , calibration , rank (graph theory) , subspace topology , sample (material) , algorithm , mathematics , gram , annihilation , computer science , statistics , mathematical analysis , combinatorics , physics , chemistry , chromatography , quantum mechanics , biology , bacteria , genetics
An improved algorithm for the generalized rank annihilation method (GRAM) is presented. GRAM is a method for multicomponent calibration using two‐dimensional instruments, such as GC‐MS. In this paper an orthonormal base is first computed and used to project the calibration and unknown sample response matrices into a lower‐dimensional subspace. The resulting generalized eigenproblem is then solved using the QZ algorithm. The result of these improvements is that GRAM is computationally more stable, particularly in the case where the calibration sample contains chemical constituents not present in the unknown sample and the unknown contains constituents not present in the calibration (the most general case).