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When the matrix order is 2 , the matrix eigenvalue problem can be solved directly starting from the matrix itself , just take a quadratic equation can be. But when the order of the matrix is higher than 3:00 , the eigenvalue problem is very difficult , the general numerical analysis solutions. So far, there has been many effective methods, such as just eigenvalues ??of the matrix can be a strong power law , all eigenvalues ??if requested , you can solve the similarity transformation , including the Jacobi iterative method and QR method , the two methods for eigenvalue problems SMEs have better results . This article will divide and conquer method applied Matrix ideological characteristics , the eigenvalues ??are asking questions divided into several sub- problems to solve , but also gives the theoretical basis of the algorithm and the original reference theorem maximum or minimum eigenvalue lies interval to be accurate and the entire theorems to be proved , then according to this theorem , combined with characteristics of symmetric tridiagonal matrix using parabolic interpolation method introduces a practical in parallel processing computer matrix eigenvalues ??new algorithms , an example for this algorithm of prayer , the results show that this algorithm is practical a broader, it can not only find all eigenvalues ??of the matrix , you can also find some arbitrarily designated interval characteristic value , and because the algorithm is suitable for parallel processing computer , which is a very economical algorithm, is ideal for high-tech adaptation algorithms. In addition, the paper also discusses the nature Householder matrix but also the promotion of this matrix and discussed the promotion of some properties of the matrix after the nature and proved.
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