| タイトル | An O(N squared) method for computing the eigensystem of N by N symmetric tridiagonal matrices by the divide and conquer approach |
| 本文（外部サイト） | http://hdl.handle.net/2060/19880009800 |
| 著者（英） | Tadmor, Eitan; Gill, Doron |
| 著者所属（英） | NASA Langley Research Center |
| 発行日 | 1988-03-01 |
| 言語 | eng |
| 内容記述 | An efficient method is proposed to solve the eigenproblem of N by N Symmetric Tridiagonal (ST) matrices. Unlike the standard eigensolvers which necessitate O(N cubed) operations to compute the eigenvectors of such ST matrices, the proposed method computes both the eigenvalues and eigenvectors with only O(N squared) operations. The method is based on serial implementation of the recently introduced Divide and Conquer (DC) algorithm. It exploits the fact that by O(N squared) of DC operations, one can compute the eigenvalues of N by N ST matrix and a finite number of pairs of successive rows of its eigenvector matrix. The rest of the eigenvectors--all of them or one at a time--are computed by linear three-term recurrence relations. Numerical examples are presented which demonstrate the superiority of the proposed method by saving an order of magnitude in execution time at the expense of sacrificing a few orders of accuracy. |
| NASA分類 | NUMERICAL ANALYSIS |
| レポートNO | 88N19184
AD-A192762
ICASE-88-19
NAS 1.26:181647
NASA-CR-181647 |
| 権利 | No Copyright |
| URI | https://repository.exst.jaxa.jp/dspace/handle/a-is/146911 |
