广义特征值问题求解的改进Ｒｉｔｚ向量法

从提高算法的稳定性和计算效率入手，采取迭代及防止漏根、多根的措施，对传统的Ｒｉｔｚ向量法进行改进，提出改进的Ｒｉｔｚ向量法。此算法仅需生成ｒ维的Ｋｒｙｌｏｖ空间，大大降低投影矩阵阶数，减少投影矩阵特征值计算时间。引入重正交方案和模态比较法，并给出Ｒｉｔｚ向量块宽ｑ与生成步数ｒ的建议取值。最后通过四参数的谱变换法，不

Improved Ritz vector method for generalized eigenvalue problems

To improve stability and efficiency,the improved Ritz vector method was presented,iteration and some effective measures avoiding root leakage or extra roots were adopted.The traditional Ritz vector method was improved.This new method only needed r-dimensional Krylov space to be constituted,greatly reduced the order number of projection matrix,decreased the eigenvalue computing time of projection matrix.Repeated orthogonality scheme and mode compare method were introduced.The values of block width q and iteration step r for Ritz vector were suggested.At last,with a four-parameter spectral transformation method,the computation efficiency and stability were greatly increased.At the same time,the applicable range of Ritz vector method was broadened.The numerical examples were given to demonstrate the validity and efficiency of the proposed method.