求反对称阵特征值的新算法 |
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引用本文: | 廉庆荣,金志英. 求反对称阵特征值的新算法[J]. 计算数学, 1987, 9(2): 200-205 |
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作者姓名: | 廉庆荣 金志英 |
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作者单位: | 大连工学院应用数学系(廉庆荣),大连工学院应用数学系(金志英) |
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摘 要: | 1971年,M.H.C.Paardekooper将对称阵的Jacobi思想推广到反对称阵,给出一个求反对称阵特征值的实用算法(简称P算法).但P算法仅考虑到矩阵的反对称性,未利用其纯虚数特征值共轭成对的性质,而且也未探讨特征值共轭对相重与否对运算量的影响.鉴于此,本文提出一个新算法,其运算量比P算法少得多. 我们先用Givens相似变换(其快速算法见§3之3.2)化反对称阵A为三对角反对称
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A NEW ALGORITHM FOR COMPUTING EIGENVALUES OF SKEW-SYMMETRIC MATRICES |
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Affiliation: | Lian Qing-rong;Jin Zhi-ying Dalian Institute of Technology |
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Abstract: | In this paper, a new algorithm for compuing eigenvalues of skew-symmetric matrices isgiven, the idea of which is different from that in [1]. Theoretically, the amount of multiplica-tions in the new algorithm is approximately from 1/30 to 1/18 and 1/12 of that in the algorithmin [1] and in the QR algorithm, respectively. Computation shows that the higher the mulplicityof the conjugate eigenvalue pairs, the less computing time the new algorithm has. |
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