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Chen, Haibo; Lv, Xianqing; Qiao, Yansong

Application of gradient descent method to the sedimentary grain-size distribution fitting. (English) Zbl 1173.86310

J. Comput. Appl. Math. 233, No. 4, 1128-1138 (2009).
Summary: Existence of a least squares solution for a sum of several weighted normal functions is proved. The gradient descent (GD) method is used to fit the measured data (i.e. the laser grain-size distribution of the sediments) with a sum of three weighted lognormal functions. The numerical results indicate that the GD method is not only easy to operate but also could effectively optimize the parameters of the fitting function with the error decreasing steadily. Meanwhile the overall fitting results are satisfactory. As a new way of data fitting, the GD method could also be used to solve other optimization problems.

Cited in 2 Documents

MSC:

86A32 Geostatistics
65D10 Numerical smoothing, curve fitting
62J02 General nonlinear regression
90C31 Sensitivity, stability, parametric optimization
62P12 Applications of statistics to environmental and related topics
93E24 Least squares and related methods for stochastic control systems

Keywords:

nonlinear least squares data fitting; gradient descent; mixture distribution of three lognormal components; laser grain-size; existence theorem
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\textit{H. Chen} et al., J. Comput. Appl. Math. 233, No. 4, 1128--1138 (2009; Zbl 1173.86310)
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References:

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