Generalized rank annihilation GRAM method

In this section we focus on methods for the quantitation of a compound in the presence of an unknown interference without the requirement that this interference should be identified first or its spectrum should be estimated. Hyphenated methods are the main application domain. The methods we discuss are generalized rank annihilation method (GRAM) and residual bilinearization (RBL). 

Chemometric methods can greatly increase the number of analyzable peaks in MDLC in particular, the generalized rank annihilation method (GRAM) can quantify overlapping peaks by deconvoluting the combined signal to those of each dimension. Standards with precise retention time are required, and there must be some resolution in both dimensions [60,61]. 

Three-way calibrations methods, such as the generalized rank annihilation method (GRAM) and parallel factor analysis (PARAFAC), are becoming increasingly prevalent tools to solve analytical challenges. The main advantage of three-way calibration is estimation of analyte concentrations in the presence of unknown, uncalibrated... 

An alternative method to solving Equation 12.3 is to reduce both Rj and R2 to square, nonsingular, nonidentity matrices by projecting each matrix independently onto the space formed jointly by the two matrices. This permits calculation of A and F, via the QZ algorithm [23] and, by extension, relative concentration estimates, Z, and estimates of the true underlying factors in the X- and Y-ways. This is known as the generalized rank annihilation method (GRAM) [24, 25],... 

FID-GRAM free induction decay generalized rank annihilation method... 

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