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188 Katharine M. Mullen, Mikas Vengris, and Ivo H.M. van Stokkumby KAUF, GP, and NUM are usable as a measure of confidence in the associated parametervalues, and allow, e.g., the construction of confidence regions about parameter estimates.The standard error estimates returned by ALS-LS do not allow inference regarding the associatedparameter estimates, which is a significant drawback in practical application. Underthe criteria of computational efficiency and goodness of standard error estimates, we thusconclude that variable projection based algorithms are advantageous over alternating leastsquaresbased techniques, and are to be preferred for application to this problem domain. Ofthe variable projection techniques, the KAUF algorithm is the least computationally expensiveas evident from comparison of the equations determining the gradient. Hence we recommendthat KAUF be considered the optimal variable projection-based technique for fittingspectrotemporal models to time-resolved spectra.6. AcknowledgmentsThis research was funded by Computational Science grant #635.000.014 from the NetherlandsOrganization for Scientific Research (NWO).References[1] Douglas M. Bates and Mary J. Lindstrom. Nonlinear least squares with conditionally linear parameters. InProceedings of the Statistical Computing Section, pages 152–157, New York, 1986. American Statistical Association.[2] Douglas M. Bates and Donald G. Watts. Nonlinear regression analysis and its applications. John Wiley & Sons,1988.[3] M. Blanco, A.C. Peinado, and J. Mas. Elucidating the composition profiles of alcoholic fermentions by use ofALS methodology. Analytica Chimica Acta, in press, 2005.[4] G. H. Golub and V. Pereyra. The differentiation of pseudoinverses and nonlinear least squares problemswhose variables separate. SIAM J. Num. Anal., 10:413–432, 1973.[5] Gene Golub and Victor Pereyra. Separable nonlinear least squares: the variable projection method and itsapplications. Inverse Problems, 19:R1–R26, April 2003.[6] G.H. Golub and V. Pereyra. The differentiation of pseudo-inverses and nonlinear least squares problemswhose variables separate. Technical report, Stanford University, Department of Computer Science, 1972.[7] L. Kaufman. A variable projection method for solving separable nonlinear least squares problems. BIT,15:49–57, 1975.[8] L. Kaufman and D. Gay. Tradeoffs in algorithms for separable and block separable nonlinear least squares. InR. Vichnevetsky and J. J. H. Miller, editors, IMACS ’91, Proceedings of the 13th World Congress on Computationaland Applied Mathematics, pages 157–158, Dublin, 1991. Criterion Press.[9] John F. Nagle. Solving complex photocycle kinetics - theory and direct method. Biophysical Journal, 59:476–487, 1991.[10] R Development Core Team. R: A language and environment for statistical computing. R Foundation for StatisticalComputing, Vienna, Austria, 2004. ISBN 3-900051-07-0.[11] Axel Ruhe and Per Ake Wedin. Algorithms for separable nonlinear least squares problems. SIAM Review,22(3):318–337, July 1980.[12] Ivo H.M. van Stokkum. Parameter precision in global analysis of time-resolved spectra. IEEE Transactionson Instrumentation and Measurement, 46(4):764–768, 1997.[13] Ivo H.M. van Stokkum, Delmar S. Larsen, and Rienk van Grondelle. Global and target analysis of timeresolvedspectra, and erratum. Biochimica et Biophysica Acta, 1657, 1658:82–104, 262, 2004.[14] Ji-Hong Wang, Philip K. Hopke, Thomas M. Hancewicz, and Shuliang L. Zhang. Application of modifiedalternating least squares regression to spectroscopic image analysis. Analytica Chimica Acta, 476:93–109, 2003.[15] H. Wold and E. Lyttkens. Nonlinear iterative partial least squares (NIPALS) estimation procedures. Bull. ISI,43:29–51, 1969.