Abstract

Construction of three kinds of QR algorithm based on optimal power evaluation model for solving the matrix eigenvalue

Author(s): Yuhuan Cui, Jingguo Qu

As the most basic, the most important knowledge system In linear algebra, matrix solution is the basis of learning and application of linear algebra. Therefore, the eigenvalues of the matrix becomes one of the focus of the study naturally. In this paper, their are a series of studies for the eigenvalues of the matrix algorithm. It starts with the concept and nature of the matrix, the eigenvalues and algorithm. The final purpose of research is the three constraint conditions. They are simple in calculation,easy understanding, accurate results. Analysis of Schmidt Orthogonalization, elementary transformation of matrix and Givens transformation of the three algorithms, thus draw the conclusion: Computing characteristic value of matrix is not only the simple problems of mathematical evaluation and calculation, but also it relates to many areas of life such as engineering and technology. In the solution process, the algorithm is more common, the most widely one. And for Schmidt Orthogonalization, elementary transformation of matrix and Givens transformation is studied, Through the construction of optimal power evaluation model, found the elementary transformation of matrix is the most suitable for matrix eigenvalue algorithm finally.