Perturbation Bounds Of The Nonnegative Definite Factor In The Polar Decomposition

The problem about matrix perturbation mainly makes study of the effect of the minor variances of matrix elements on the problem solution of matrix. With profound theoretical significance and the extensive application background, it is not only closely related with the analysis and processing of calculation results of a lot of numerical analysis, but also plays an important role in structural mechanics, quantum mechanics, engineering design and computational physics.In the second half of the last century, the theory of matrix perturbation overseas enjoyed sufficient development, and the system was relatively complete. After the mid1980s, the efforts made by a group of mathematicians in China in this area made a breakthrough progress, and made important contributions to the applications of matrix perturbation problems in other disciplines.The perturbation of polar decomposition is an integral part of the matrix perturbation theory. The article mainly makes study of the semi-positive definite factor in the additive perturbation, and figures out new perturbation bounds. The details are stated as follows:Firstly, it gives an introduction to the main contents studied in this paper and the present situation of relevant research results at home and abroad.Secondly, it gives an introduction to some fundamental knowledge, important concepts and theorems in the matrix perturbation analysis.Finally, it gives an introduction to some important concepts about the polar decomposition, makes study of the perturbation bounds of the positive definite factor and the combined perturbation bounds of the polar decomposition. In the article, the existing results are improved and promoted.