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Choleskymultivariate decomposition algorithmfor infrared spectrometric determination of active components in laundry detergent powder

Mohammadreza Khanmohammadi, Mohammadhossein Ahmadi Azghandi

A new calibration method based on of Cholesky decomposition (CD) has been introduced. It is the decomposition of a positive-definitematrix into the product of a lower triangularmatrix and its conjugate transpose. This approach has been utilized to overcome the problem of serious spectral overlapping during the infrared spectrometric determination of sodium tripolyphosphate, sodium sulfate and sodium carbonate in laundry detergent powders. Comparing the root mean square error of prediction in Choleskymethod and those obtained by partial least squares regression, it was concluded that Cholesky algorithmwould offer more reliable prediction efficiency. It is alsomentionable that Cholesky is a rapid data processing technique which speeds reduces the order of matrices.