Wiscombe W.J. and Evans J., (1977) Exponential sum-fitting of radiative transmission function. J. Comput. Phys., 24, pp. 416-444  Home/Search   Document Not in Database   Summary   Related Articles   Check

....logarithmic regression has been used iteratively on the residual. The procedure is to first identify one term. Then subtract this term from the data series and apply logarithmic regression to the difference and refine a by linear least squares. Wiscombe and Evans does not recommend this method [21]. A special method for two terms is to apply logarithmic regression to the transient and the tail. See Steyn and Wyk [20] Crucial to this is where to define the interval for the transient and an interval for the tail. 2.2 Weighted least squares Of more interest would be to have an analytically ....

W. J. Wiscombe and J. W. Evans. Exponential-Sum fitting of radiative transmission functions. Computational Physics, 24(4):416--444, August 1977.

.... easy to watch . Their results are often not very accurate, but can be used as an initial guess for more sophisticated iterative methods. A Review of the Problem of Fitting Positive Exponential Sums to Empirical Data 4 Graphical methods are discussed by Steyn and Wyk [85] and Wiscombe and Evans [88]. The main idea in the parameter identification is: Plot the curve (t; ln y) Study if the tail stabilizes along a straight line. Then the slope of the tail is Gammab 1 . Find a 1 as a linear least squares estimate using the tail. Now one term a 1 Delta exp ( Gammab 1 t) in (1) is identified. ....

....repeat the procedure on the plot (t; ln e y) to get Gammab 2 . Find new values of all a i by simultaneous linear least squares fit using all the so far obtained b i . Steyn et al. 85] does not go this far. They treat only the cases with one or two terms identified by hand . Wiscombe and Evans [88] reports that Avrett and Hummer [8] and Hunt and Grant [40] has made something like the procedure above. They report that this method usually fails when tried on the problem of identifying more than two terms. An explanation to this failure is found when studying a Taylor expansion. First write y ....

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W. J. Wiscombe and J. W. Evans. Exponential-Sum fitting of radiative transmission functions. Computational Physics, 24(4):416--444, August 1977.

....imaginary exponents in complex noise [18] Real exponential fitting is one of the most important, difficult and frequently occuring problems of applied data analysis. Applications include radioactive decay [38] compartment models [2, Chapter 5] 37, Chapter 8] and atmospheric transfer functions [46]. Estimation of the ff j and fi j is well known to be numerically difficult [19, p. 276] 43] 37, Section 3.4] General purpose algorithms often have great difficulty in converging to a minimum of the sums of squares. This can be caused by difficulty in choosing initial values, ill conditioning ....

....the algorithm is concerned, but may return a pair of damped sinusoids in place of two exponentials which are coalescing. In some applications the restriction to positive coefficients ff j is natural. A convex cone characterization is then possible, and special algorithms have been proposed in [6] [46] [15] 10] 35] We prefer to treat the general problem with freely varying coefficients since this is appropriate for most compartment models. A common attempt to reduce the difficulty of the general problem has been to treat it as a separable regression, i.e. to estimate the coefficients by ....

W. J. Wiscombe and J. W. Evans, Exponential-sum fitting of radiative transmission functions, J. Comp. Physics, 24 (1977), pp. 416--444.

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Wiscombe W.J. and Evans J., (1977) Exponential sum-fitting of radiative transmission function. J. Comput. Phys., 24, pp. 416-444

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