Application of gradient descent method to the sedimentary grain-size distribution fitting

Authors:
Haibo Chen;Xianqing Lv;Yansong Qiao
Affiliations:
Laboratory of Physical Oceanography, Ocean University of China, Qingdao 266100, China;Laboratory of Physical Oceanography, Ocean University of China, Qingdao 266100, China;Institute of Geomechanics, Chinese Academy of Geological Sciences, Beijing 100081, China
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

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Abstract

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.