Studies on matrix diagonalization by solving nonlinear systems

点击翻译按钮获取中文摘要

The matrix diagonalizations, for example eigenvalue decomposition, singular value decomposition, are basic topics in linear algebra, and they also important tools in various fields. In this research, we developed new method, which is called the hyperplane-constrained method. This method can obtain matrix diagonalization by solving the nonlinear systems, which are constrained on hyperplanes, by the Newton method. The problems on selecting initial vectors of the Newton method is avoided by suitable selecting the normal vectors of the hyperplanes.