块(置换群论)
最小二乘函数近似
大地测量学
数学
地理
广义最小二乘法
算法
统计
地图学
组合数学
估计员
作者
Vahid Mahboub,Somayeh Ebrahimzadeh
出处
期刊:Survey Review
[Informa]
日期:2021-09-02
卷期号:54 (387): 479-489
被引量:3
标识
DOI:10.1080/00396265.2021.1970916
摘要
In this contribution two algorithms are developed to solve non-linear system of equations which can contain a large number of measurements. These algorithms are based on nonlinear block least-squares (BLS). Although block least squares was investigated by some researchers, the non-linear case was not examined by now. The first algorithm is proposed to solve a special case of non-linear problems that do not require linearization. Such an algorithm can be called total block least-squares. The second algorithm is based on linearization within a general nonlinear mixed model using a new notation which is in agreement with the rigorous linearization presented by Pope. Both of these algorithms can handle constraints on the parameters. By use of these algorithms, big data processing is feasible with inexpensive computers. Furthermore, expensive processors can solve systems with a large number of equations faster. Two case studies with more than 120,000 equations show that fast and accurate computations are possible by applying these algorithms without any loss of accuracy.
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