自洽场方法中广义本征值方程求解及其C++程序设计  

Programming in C++ to solve the general eigenvalue equation of self-consistent field

作　　者：孙世军[1,2] 彭承琳[1] 万小萍[1] 王星[1] 张思杰[1] 

机构地区：[1]重庆大学生物工程学院,国家教育部生物力学与组织工程重点实验室,重庆400044 [2]湛江师范学院信息科技学院

出　　处：《计算机与应用化学》2006年第7期607-610,共4页Computers and Applied Chemistry

基　　金：国家自然科学基金(30470469)

摘　　要：本文研究自洽场方法中广义本征值方程求解的算法,并设计相应的C++程序来实现该算法。首先对重叠矩阵进行分解,并将广义本征值方程化为标准的本征值方程,再利用Householder变换将上一步变换所得的矩阵化为对称三对角矩阵,进而用QL方法求解这个三对角矩阵的本征值和本征矢量,从而得到自洽场方法中广义本征值方程的本征值和本征矢量。The method of solving the general eigenvalue equation in the serf-consistent field （SCF） is researched in this article, and the program in C＋＋ is developed to implement it. Firstly, overlap matrix is decomposed to convert the general eigenvalue equation into the standard eigenvalue equation. Secondarily, by using Householder＇s transform the matrix obtained from last transform is converted into a symmetric tridiagonal matrix, then by using QL algorithm the eigenvalues and eigenvectors of the tridiagonal matrix is worked out. Thus, the eigenvalues and eigenvectors of the general eigenvalue equation are worked out.

关 键 词：自洽场方法 广义本征值方程 Householder变换 QL方法 C++程序设计 

分 类 号：O641[理学—物理化学]