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https://ah.lib.nccu.edu.tw/handle/140.119/89759| 題名: | QR與LR算則之位移策略 On the shift strategies for the QR and LR algorithms |
作者: | 黃義哲 HUANG, YI-ZHE |
貢獻者: | 王太林 WANG, TAI-LIN 黃義哲 HUANG, YI-ZHE |
關鍵詞: | 位移策略 特徵向量 特徵值 QR algorithm, LR algorithm, modified Cholesky algorithm. |
日期: | 1992 | 上傳時間: | 2-May-2016 | 摘要: | 用QR與LR迭代法求矩陣特徵值與特徵向量之過程中，前人曾提出位移策略以加速其收斂速度，其中最有效的是Wilkinson 移位值。在此我們希望尋求能使收斂更快速的位移值。 Abstract |
參考文獻: | References:\r\n[l] Dekker, T . J. and Traub, J. F., 1971. \"The Shifted QR Algorithm for Hermitian\r\nMatrices.\" Linear Algebra and Its Applications, 4:137-154\r\n[2] Dubrulle, A., 1970. \"A Short Note on the Implicit QL Algorithm for Symmetric\r\nTridiagonal Matrix.\" Numer. Math. , 15 :450.\r\n[3] Golub, G. H. and Van Loan, C. F. , 1989. Matrix Computations. 2nd edition,\r\nBaltimore, MD: The Johns Hopkins University Press.\r\n[4] Jiang, E. and Zheng, Z., 1985. \"A New Shift of the QL Algorithm for Irreducible\r\nSymmetric Tridiagonal Matrices.\" Linear Algebra and Its Applications,65:261-272.\r\n[5] Ortega, J. M. and Kaiser, H. F., 1963. \"The LLT and QR Methods for Symmetric\r\nTridiagonal matrices.\" Computer Journal, 99-101.\r\n[6] Parlett, B. N. , 1964. \"The Development and Use of Methods of LR Type.\"\r\nSIAM Review, 6:275-295 .\r\n[7] Parlett, B. N., 1966. \"Singular and Invariant Matrices Under the QR Transformation. \" Math. Comp., 611-615.\r\n[8] Parlett, B. N., 1980. The Semmetric Eigenvalue Problem. Prentice-Hall Inc. ,\r\nEnglewood Cliffs 1980.\r\n[9] Rutishauser, H. and Schwarz, H. R., 1963. \"The LR Transformation Method\r\nfor Symmetric Matrices.\" Numer. Math. 5:273-289.\r\n[10] Saad, Y. , 1974, \"Shift of Origin for the QR Algorithm.\" Toronto: Proceedings\r\nIFIP Congress.\r\n[11] Smith, B. T. and Boyle, J. M., 1974. Matrix Eigensystem Routines - EISPACK\r\nGuide, Springer Verlag.\r\n[12] `Ward, R. C. and Gray, L. J ., 1978. \"Eigensystem Computation for Skew-Symmetric Matrices and a Class of Symmetric Matrices.\" A CM Trans. on\r\nMath. Software , 4:278-285 .\r\n[13] Wilkinson, J. H. and Reisch, C., 1961. Handbook for A`l?tomatric Computation.\r\nVolum. II. Linear Algebra, Springer Verlag.\r\n[14] Wilkinson, J. H. , 1968. \"Global Convergence of Tridiagonal QR Algorithm\r\nwith Origin Shifts.\" Linear Algebra and Its Applications, 1:409-420.\r\nNotation Convention:\r\n(1) CHOLESKY: This subroutine is the implementation of the modified LLT\r\nalgorithm.\r\n(2)imTQLl: This subroutine from the EISPACK computes the eigenvalues.\r\nby the implicit QL algorithm.\r\n(3) imTQL2: This subroutine from the EISPACK computes the eigenvalues\r\nand eigenvectors at the same tims by the implicit QL method.\r\n(4) imTQL2s4l: This routine first computes eigenvalues by CHOLESKY and\r\nthen uses these eigenvalues as shifts in imTQL2.\r\n(5) imTQL2s42: This subroutine makes the use of imTQL1 to compute the\r\neigenvalues and then uses these computed values as shifts in imTQL2 . .\r\n(6) TQL1: This subroutine from the EISPACK computes eigenvalues by the\r\nQL method.\r\n(7) TQL1s31, TQL1s32, TQL1s33 : These subroutines are the test of the use\r\nof 83 , described in section 3.\r\n(8) TQL2: This subroutine from the EISPACK computes eigenvalues and\r\neigenvectors simultaneously by the QL method.\r\n(9) TQL2s41: This subroutine calculate eigenvalues by CHOLESKY at first\r\nand then uses these eigenvalues as shifts in TQL2.\r\n(1 0) TQL2s42: This subroutine uses eigenvalues computed by TQL1 as shifts\r\nin TQL2. | 描述: | 碩士 國立政治大學 應用數學系 |
資料來源: | http://thesis.lib.nccu.edu.tw/record/#B2002004735 | 資料類型: | thesis |
| Appears in Collections: | 學位論文 |
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