• 论文 • 上一篇    

解实对称矩阵特征值问题的Jacobi算法

邓建新   

  1. 中国科学院计算中心
  • 出版日期:1981-02-20 发布日期:1981-02-20

邓建新. 解实对称矩阵特征值问题的Jacobi算法[J]. 数值计算与计算机应用, 1981, 2(2): 122-128.

THE JACOBI METHOD OF SOLVING EIGENVALUE PROBLEM OF A REAL SYMMETRIC MATRIX

  1. Deng Jian-xin Computing Centre, Academia Sinica
  • Online:1981-02-20 Published:1981-02-20
求解n阶实对称阵A的特征值问题Ax=λx的Jacobi方法,是用一系列平面旋转变换化A为对角型,从而得到特征值和特征向量的.假设A_0=A,A_k=R_kA_(k-1)R_k~T,k=1,2,3,…,当k→∞时,A_k趋向于固定的对角型.简记某次变换为
In this paper, some computing schemes, fast algorithm, choices of plane rotations forJacobi method are analyzed and compared, and in addition the numerieal tests are pro-cessed. A powerful algorithm and its computer program is recommended, which mayproduce more accurate results and usually save time at least 30% when compared withcommon program.
()

[1] W. M. Gentleman, Least Squares Computations by Givens Transformations Without square roots, J. Inst. Math. Appl. 12 (1973) , 329-336.
[2] W. M. Gentleman, Error analysis of QR decompositions by givens transformations, Lin. Alg. Appl. 10(1975) , 189-197.
[3] S. Hammarling, A note on modifications to the givens plane rotation, J. Inst. Math. Applis. 13 (1974) , 215-218.
[4] G. W. Stewart, The economical storage of plane rotations, Numer. Math. 25(1976) 137-138.
[5] J. H. Wilkinson, Some recent advances is numerical linear algebra, The Stete of the Artin Numerical Analysis, Edited by. D. A. H. Jacobs, 1977.
[6] 曹维潞,数值线性代数发展概况,1978年全国数值代数学术交流会报告.
[7] 谭领,代数特征值问题(讲义),1979年厦门数值代数讨论会报告.
[8] 沈启钧,平面旋转变换的快速算法,1979年全国计算数学年会报告.
[9] J. H. Wilkinson, The algebraic eigenvaluproblem, 1965.
[10] 冯康,数值计算方法,国防工业出版社,1978年.
[11] J. H. Wilkinson, C. Reinsch, Linear algebra, 1971.
No related articles found!
阅读次数
全文


摘要