广义Jacobi方法的优化算法

AN OPTIMAL ALGORITHM OF THE GENERALIZED JACOBI METHOD

针对有限单元法结构分析中的对称方阵广义特征值问题,提出广义Jacobi方法的一种优化算法.在该算法中,对非对角元素的阈值判断和扫描圈迭代的收敛准则采用了与以往文献中不同的新颖措施,使得该算法不仅适用于对称正定方阵,而且还可应用于全部特征值均为实数时任意对称方阵的广义特征值问题.并对这一算法给出了证明.

An optimal algorithm of the generalized Jacobi method is developed to solve the generalized eigenproblems in the finite element analysis of structural problems.Novel operations in this optimal algorithm are adopted to define the threshold estimation for the off-diagonal elements and the convergency criteria in the sweeping iterations,so that the present algorithm is applicable to the original structural problems,not only with the positive-definite matrices,but also with the general symmetric matrices so long as their eigenvalues are all real numbers.This paper has proved the optimal algorithm mathematically.