逐个加入初始向量的Ritz向量法

THE MQDIFIED RITZ VECTOR METHOD OF INTRODUCING INITIAL VECTORS ONE BY ONE

本文综合了子空间迭代法和 Ritz 向量法的优点,采用多个初始向量逐个加入迭代的方式,提出了一种计算大型结构部分模态的改进方法.该法仍保持单个向量反选代的特点,在计算量上与 Ritz 向量法相同,而比子空间迭代法少得多,精度也不低于子空间迭代法.由于在理论上保证对重特征值的收钦性,因此在相同的迭代次数下,本法的精度优于一般的 Ritz 向量法和 Lanczos 法.

In a modified scheme advanced,a series of initial vectors are employed in the form of one by one iteration.The method takes and combines the advant- ages of both the subspace iteration method and Ritz vecter method.A method for partial eigen-solution of Iarge structure is put forward.Compared with the Ritz vector method,the scheme still keeps the feature of using sidgle vector for inverse iteration.So the computing time of this scheme may be similar to that of Ritz method,but quite less than that of subspace iteration method.Yet the scheme may compete with the Iatter in accuracy,since the convergence for multiple eigenvalue is proved theoretically.Compared in the same turns of iteration the accuracy of this scheme is superior to that of both Rite vector method and Ianczos method.