大型广义特征值问题的动力降阶迭代法

 本文在Guyan、Kuhar等人工作基础上,提出通过动力降阶和迭代,对大型广义特征值问题实施逼近求解的一个新方法,以能对大型、复杂动力系统实施动力分析。既解决计算机容量不足,又保证精度,亦不耗时过多。通过实际使用,证明该方法的有效性。

A DYNAMIC REDUCING ITERATIVE METHOD FOR SOLVING LARGE GENERALIZED EIGENVALUE PROBLEMS

A new reduction method for solving large generalized eigenvalue problems is presented, which can Not only overcome difficulties of computer capacity and give the required accuracy but also save much computer run time.The "dynamic transformation" method suggested by Kuhar is an improvement on Guyan's reduction method. But this method is Now only applied to the eigenvalue problems deduced from modal synthesis techniques and its general mathematical consideration has Not appeared yet.This paper is devoted to the mathematical discussion of Kuhar's idea and deals with general generalized eigenvalue problems. Furthermore, it proposes a new reduction method, called "dynamic reducing iterative method", by virtue of which it is possible to approximate to the actual eigenvalue with necessary accuracy. The convergence of the iterative process has been proved yet. A general criterion of partition into master and slave coordinate sets is also found. Some results of application of the method are reported to demon?. strate its effectiveness.