LU decomposition is a triangular decomposition approach of non-singular matrix, and the digital image can be seen as a matrix.

LU分解是一种将非奇异矩阵进行三角分解的方法，而数字图像也可以看作矩阵。

Based on the original precise integration method, the problem that singular matrix appears in non-homogeneous equation was discussed.

在原有精细积分法的基础上，对非齐次方程出现奇异矩阵的问题进行探讨。

Necessary cycle detection is added to avoid the singular matrix appearing after gross error compensation,. Simulation results verify the effectiveness of modified algorithm.

通过加入必要的回路检测，避免了幅度补偿后矩阵奇异性的产生，仿真结果表明了改进算法的有效性。

Furthermore, each element in the singular stiffness matrix can be expressed by some more simple analytic formulas.

而且奇异单元刚度矩阵中的各元素可以用较简单的分析式表出。

Using matrix iteration methods, the eigenvector derivatives can be iterated directly, solving the singular sensitivity equation can be avoided.

采用矩阵迭代法可以直接迭代计算特征向量导数，避免了对奇异灵敏度方程的求解。