Divide and conquer algorithm for computer simulation and application in the matrix eigenvalue problem

DC is a divide and conquers method for short. Its basic idea is to divide the given real symmetric tridiagonal matrix A into two lower-order submatrix A1 , A2 first, then glue the eigenvalues of the two submatrixes together and find the eigenvalue and eigenvector of the original symmetric triangular matrix by means of some calculations. It is that we solve the submatrix eigenvalue problem, and then pose a question easy to answer than the original eigenvalue problem. Finally we uses computer to simulate, using mathematical software programming to solve the eigenvalues of each submatrix separately.