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近十多年来发展起来的求解大型稀疏对称矩阵部分极端特征值的Lanczos方法的高度有效性早已为工程界人士所瞩目,但是,由于该方法在理论上和技术上的复杂性,经细致的理论探讨和大量试验之后,直至近几年国内外才着手通用化工作。Lanczos方法在大多数情况下的计算速度大大快于目前流行的子空间迭代法,因此大有取而代之之势。本文向读者推荐求解广义特征值问题的经过精心编制的Lanczos方法通用程序。文中首先简要地介绍一下方法的理论背景;然后介绍程序及其使用时的操作方法,对软件感兴趣的读者还能发现这个根据现代软件要求编制的程序的许多优良性能,文章末尾,通过实际问题的计算比较,读者可以看到,由于谱分布的特点,在结构动力等其它一些特征问题中,谱变换广义Lanczos方法的速度往往能数倍于传统的子空间迭代法。
The highly effective method of Lanczos method developed for the extreme eigenvalues of large-scale sparse symmetric matrices, which has been developed in the past ten years, has long been paid attention to by engineers. However, due to the theoretical and technical complexity of the method, After theoretical discussions and extensive tests, it was not until recent years that the generalization work began at home and abroad. Lanczos method in most cases the computational speed much faster than the current popular subspace iterative method, so a great alternative. This article recommends to readers the well-crafted Lanczos Method Common Procedure for solving generalized eigenvalue problems. The paper first briefly introduces the theoretical background of the method. Then it introduces the program and how to use it. The readers who are interested in the software can also find many excellent performances of the program compiled according to modern software requirements. At the end of the article, , Readers can see that due to the characteristics of spectral distribution, the spectral transform generalized Lanczos method tends to be several times faster than the traditional subspace iteration method in other feature problems such as structural dynamics.