Gram-Schmidt algorithm

Generating the ortho-normalized orbital eigen-waves, here according with the Gram-Schmidt algorithm among shells and sub-shells ... 

ELCD electrolytic conductivity detector GS Gram-Schmidt (algorithm)... 

Since the bands that are measured in GC/FT-IR experiments are almost invariably very weak, their integrated absorbance varies linearly with the quantity of each analyte injected. On the other hand, when chromatograms are constructed using the Gram-Schmidt algorithm, the signal that is measured is proportional to the absorp-tance, 1 — T v), of each band. Since transmittance and absorbance are related as... 

Furthermore, the basis set is easily transformed to yield a new set 6, with the property that (6, 6j) = Si Such a set is called orthonormal. The standard procedure is the Gram-Schmidt ON-algorithm ... 

Kroonenberg PM, ten Berge JMF, Brouwer P, Kiers HAL, Gram-Schmidt versus Bauer-Rutishauser in alternating least-squares algorithms for three-mode principal component analysis, Computation Statistics Quarterly, 1989, 2, 81-87. 

Figure 4a is the spectrum of supercritical CO2 (same as Figure 1) plotted to visually compare the two spectra. It is important to realize that the Gram-Schmidt Plus algorithm removes the CO2 interference from the reconstructed chromatograms only. It does not affect the actual FT-IR spectra in any way. 

Of all of the methods, including the modified Gram-Schmidt and Householder algorithm (Buzzi-Ferraris and Manenti, 2010a), the technique proposed by Powell (1968) is the preferred one. 

Gram-Schmidt procedure An algorithm for obtaining a set of orthonormal functions from a set of signals. 

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