A new calibration method based on of Cholesky decomposition (CD) has been introduced. It is the decomposition of a positive-definite matrix into the product of a lower triangular matrix 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

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... holesky method and those obtained by partial least squares regression, it was concluded that Cholesky algorithm would offer more reliable prediction efficiency. It is also mentionable that Cholesky is a rapid data processing technique which speeds reduces the order of matrices. 