By means of impulse response and matrix perturbation method of nonlinear system, the author finds that the response statistics of a nonlinear system are subjected to random excitation.

A complex modal matrix perturbation method for symmetrical systems is deduced for optimum analysis of non-proportionally damped structures.

When crack expanding problem is studied,a high efficiency semi-analytical matrix perturbation method is put forward.

A general matrix perturbation method for complex modes using singular value decomposition;

The principle of finite element matrix perturbation programming is introduced,and the measures for improving numerical calcuating speed are investigated in this paper.

Information-sharing approach to federated filtering based on matrix perturbation theory;

Recursive PCA algorithm based on rank-one matrix perturbation

Based on the matrix perturbation and Epsilon-algorithm, a new static displacement reanalysis for modified structure was given.

The complex matrix is given by the form of the real-part and imaginary part matix decomposition formula sum and using the perturbation matrix to seek the inverse formula and the iteration formula of the complex matrix inversion given in the paper is established.

In the paper, the author uses the operational rule of the matrix and the definition of the inverse matrix to give a concrete fomula of the inverse matrix for the perturbation matrix(A+δuv~T) and its general form by alternation(A+UBV).

The thesis introduces ways to seek approximate counting of perturbation matrix proper value when there is slight change in non_self_accompanied system matrix, and lists the error grades caused by various methods, and compares the accuracy of the results respectively.