CAJ | 학술논문

最小二乘是测量平差最主要的手段,该方法需要对法方程系数阵求逆.介绍对此类实对称矩阵求逆的Jacobi数值方法,通过正交矩阵变换,将实对称矩阵的非对角元变为零,求得特征根和特征向量,从而使求逆变得非常容易,并且有利于判断矩阵是否奇异以及秩亏数是多少.此方法为数值方法,易于计算机实现.
최소이승시측량평차최주요적수단,해방법수요대법방정계수진구역.개소대차류실대칭구진구역적Jacobi수치방법,통과정교구진변환,장실대칭구진적비대각원변위령,구득특정근화특정향량,종이사구역변득비상용역,병차유리우판단구진시부기이이급질우수시다소.차방법위수치방법,역우계산궤실현.
Least square is general approach in surveying adjustment, where inversion of normal equation is inevitable. The algorithm of Jacobi numerical method for inversing real symmetry matrix is introduced. By orthogonal transformation, the non diagonal elements can be changed to zero and eigenvalues with corresponding eigenvectors are obtained. It makes the inversion of matrix very easy. The ranks of normal equation are the number of non-zero eigenvalues. The approach is numerical so can be realized easily with a computer.