DOI: 10.1002/cem.1180030306. An improved algorithm for the generalized rank annihilation method

An improved algorithm for the generalized rank annihilation method

10.1002/cem.1180030306

Crossref journal-article

Wiley

Journal of Chemometrics (311)

Abstract

AbstractAn 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).

Bibliography

Wilson, B. E., Sanchez, E., & Kowalski, B. R. (1989). An improved algorithm for the generalized rank annihilation method. Journal of Chemometrics, 3(3), 493â498. Portico.

Authors 3

Bruce E. Wilson (first)
Eugenio Sanchez (additional)
Bruce R. Kowalski (additional)

References 21 Referenced 122

10.1021/ac00293a054
10.1021/ac50030a026
10.1016/S0003-2670(00)85643-3
10.1016/S0021-9673(01)94629-1
10.1016/S0021-9673(01)94630-8
E.Sanchez R. J.PellandB. R.Kowalski FACSS 1988 Boston MA 1988.
10.1093/chromsci/21.5.229
10.1021/ac50057a018
10.1021/ac00224a024
10.1021/ac00262a006
10.1021/ac00281a030
B. E.Wilson W.LindbergandB. R.Kowalski JACS in press (1988).
{'key': 'e_1_2_1_14_2', 'volume-title': 'Generalized Inverse of Matrices and it Applications', 'author': 'Rao C. R.', 'year': '1971'} / Generalized Inverse of Matrices and it Applications by Rao C. R. (1971)
10.1137/0710024
10.1137/0712062
10.1002/cem.1180020405
A.LorberandB. R.Kowalski J. Chemometrics in press.
E.Sanchez Ph. D. Dissertation University of Washington Seattle WA (1987).
10.1080/00401706.1978.10489693
{'key': 'e_1_2_1_21_2', 'volume': '185', 'author': 'Geladi P.', 'year': '1986', 'journal-title': 'Anal Chim. Acta'} / Anal Chim. Acta by Geladi P. (1986)
{'key': 'e_1_2_1_22_2', 'volume-title': 'Matrix Computations', 'author': 'Golub G. H.', 'year': '1985'} / Matrix Computations by Golub G. H. (1985)

Dates

Type	When
Created	20 years, 3 months ago (May 28, 2005, 8:47 p.m.)
Deposited	1 year, 9 months ago (Oct. 31, 2023, 12:36 p.m.)
Indexed	1 month ago (July 30, 2025, 8:24 p.m.)
Issued	36 years, 2 months ago (June 1, 1989)
Published	36 years, 2 months ago (June 1, 1989)
Published Online	20 years, 5 months ago (March 30, 2005)
Published Print	36 years, 2 months ago (June 1, 1989)

Funders 0

None

BibTeX

@article{Wilson_1989, title={An improved algorithm for the generalized rank annihilation method}, volume={3}, ISSN={1099-128X}, url={http://dx.doi.org/10.1002/cem.1180030306}, DOI={10.1002/cem.1180030306}, number={3}, journal={Journal of Chemometrics}, publisher={Wiley}, author={Wilson, Bruce E. and Sanchez, Eugenio and Kowalski, Bruce R.}, year={1989}, month=jun, pages={493–498} }

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