The first method tested is the Derivative Matrix Isopotential Synchronous Fluorimetry (DMISF). Two methods powerful in resolving spectral components are compared in this paper. A method which can provide information about spectrally hidden components in mixtures is very useful. Several methods are available to calculate the constituents' concentrations in moderately complex mixtures.
Makkai, Géza Buzády, Andrea Erostyák, Jánosĭetermination of concentrations of spectrally overlapping compounds has special difficulties. Sensitivity test of derivative matrix isopotential synchronous fluorimetry and least squares fitting methods. The approach consists of iteratively performing steps of existing algorithms for ordinary least squares fitting of the same model and is based on maximizing a function that majorizes WLS loss function. Weighted Least Squares Fitting Using Ordinary Least Squares Algorithms.ĮRIC Educational Resources Information CenterĪ general approach for fitting a model to a data matrix by weighted least squares (WLS) is studied. It has been implemented under DOS 3.2.1 using 23K of RAM.
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AKLSQF was written for an IBM PC X/AT or compatible using Microsoft's Quick Basic compiler. All computations in the program are carried out under Double Precision format for real numbers and under long integer format for integers to provide the maximum accuracy possible. In general, the program can produce a curve fitting up to a 100 degree polynomial.
At every step the polynomial as well as the least squares fitting error is printed to the screen. The degree of the polynomial used for fitting is then increased successively until the error criterion specified by the user is met. If an error tolerance is specified, the program starts with a polynomial of degree 1 and computes the least squares fit error. The result is then reduced to a regular polynomial using Sterling numbers of the first kind. First, the data points are least squares fitted using the orthogonal factorial polynomials. AKLSQF produces the least squares polynomial in two steps. The data may be supplied to the routine either by direct keyboard entry or via a file. In both cases AKLSQF returns the polynomial and the actual least squares fit error incurred in the operation. The program allows the user to specify the tolerable least squares error in the fitting or allows the user to specify the polynomial degree. The Least Squares Curve Fitting program, AKLSQF, computes the polynomial which will least square fit uniformly spaced data easily and efficiently. It is stressed that the least- squares method is inapplicable to the non-Gaussian noise cases when the noise level is larger than 5%. It is observed that the non-Gaussian noises are less accurately fitted than the Gaussian noise, but the stretched Gaussian cases appear to perform better than the Lévy noise cases. Lévy and stretched Gaussian distributions have many applications in fractional and fractal calculus.
We add different levels of the two typical non-Gaussian noises, Lévy and stretched Gaussian noises, to exact value of the selected functions including linear equations, polynomial and exponential equations, and the maximum absolute and the mean square errors are calculated for the different cases. This study is to investigate the feasibility of least square method in fitting non-Gaussian noise data. Written for an IBM PC X/AT or compatible using Microsoft's Quick Basic compiler.įeasibility study on the least square method for fitting non-Gaussian noise data Data supplied to routine either by direct keyboard entry or via file. AKLSQF returns polynomial and actual least- squares-fit error incurred in operation. Enables user to specify tolerable least- squares error in fit or degree of polynomial. Least Squares Curve Fitting program, AKLSQF, easily and efficiently computes polynomial providing least- squares best fit to uniformly spaced data.
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