在均衡自由大地网中通过搜索法寻找目标函数的全局最小值以确定伪逆矩阵

G.G. Shevshenko, N.A. Naumova, M. Bryn
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引用次数: 0

摘要

在根据非线性编程搜索法评估均衡自由大地测量网络的精度时,会形成一个未知数法式方程系数的退化矩阵。它必须是伪逆矩阵,以便计算均衡参数之一的逆权重。根据上述非线性编程技术计算伪逆矩阵的数学过程,在均衡自由大地构造时,可能会出现最小化步骤选择错误或所需数字阵列中的近似值设置粗糙的情况。这可能导致找到局部而非全局最小值,以及算法循环。作者提供了公式的结论,并证实了所需矩阵元素发生变化的条件,这样目标函数的值要么尽可能接近全局最小值,要么表明不可能达到全局最小值。通过一个测试实例证实了所提出的条件和推导公式的正确性
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Looking for the global minimum of the objective function to determine the pseudoinverse matrix through the search method at equalizing free geodesic networks
When evaluating the accuracy of equalized free geodetic networks based on the search method of nonlinear programming, a degenerate matrix of unknowns’ normal equations coefficients is formed. It must be pseudoinverse in order to calculate the inverse weight one of the equalized parameters. Performing a mathematical procedure for calculating a pseudoinverse matrix based on the mentioned technology of nonlinear programming at equalizing free geodetic constructions, a situation may arise when the minimization step is incorrectly selected or the approximate values in the desired array of numbers are set roughly. It can lead to finding a local, not a global minimum, as well as to cycling the algorithm. The authors provide the conclusion of the formula and substantiate the conditions on which the elements of the required matrix change, so that the value of the objective function either comes as close as possible to the global minimum, or indicates that it is impossible to achieve it. The correctness of the proposed conditions and the derived formula are confirmed by a test example
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