同伦连续法求解矩阵特征值的研究

On Homotopy Continuation Method to Matrix Eigen-value

研究了同伦连续法在求解举证特征值上的应用思路,证明了求解矩阵特征值过程中,构造参数方程的三个数学性质,在matcont中用同伦法求解了两个类型矩阵的特征值,同时在mat lab中用QR分解进行求解,实验显示:同伦法和QR分解计算的结果非常接近。

In this paper, the application of homotopy continuation method to matrix eigen -value is dis- cussed; and the mathematical nature of parameter equations which are constructed during the course of matrix eigen - value is also proved. Two kinds of matrix eigen - value are solved with homotopy continuation method in mat eont, QR is used to evaluate matrix eigenvalue at the same time in mat lab. The experiment shows that the re- suits of the two ways are very small.