论文标题
D维空间中最小成方误差方法的新公式，并将映射到参数线
A New Formulation for Total Least Square Error Method in d-dimensional Space with Mapping to a Parametric Line
论文作者
论文摘要
有许多基于最小平方误（LSE）或总正方形误差（TLSE）方法的实际应用。通常，由于其简单性，使用标准最小平方误差，但不是最佳解决方案，因为它不会优化距离，而是距离的平方。尊重距离测量的正交性的TLSE方法是在D维空间中计算的，即E2 A线P中给出的点P中的E2中给出的点。对于E3中给出的点，在E3中的Rho中给出了平面，可以找到拟合TLSE标准。但是，物理科学中的某些任务导致问题略有不同。在本文中，当在E3中给出数据时，引入了一种新的TSLE方法来解决问题，并且将发现E3中的一条线P适合TLSE标准。提出的方法适用于一般维情况，即在E^d中给出点时，可以找到线E^d。该公式与TLSE公式不同。
There are many practical applications based on the Least Square Error (LSE) or Total Least Square Error (TLSE) methods. Usually the standard least square error is used due to its simplicity, but it is not an optimal solution, as it does not optimize distance, but square of a distance. The TLSE method, respecting the orthogonality of a distance measurement, is computed in d-dimensional space, i.e. for points given in E2 a line p in E2, resp. for points given in E3 a plane in rho in E3, fitting the TLSE criteria are found. However, some tasks in physical sciences lead to a slightly different problem. In this paper, a new TSLE method is introduced for solving a problem when data are given in E3 and a line p in E3 is to be found fitting the TLSE criterion. The presented approach is applicable for a general -dimensional case, i.e. when points are given in E^d a line E^d is to be found. This formulation is different from the TLSE formulation.
