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題名 線性三對角方程組之平行解法
Parallel Algorithm for Linear Tridiagonal System Solver作者 林伯勳
Lin, Frank貢獻者 施東河
Shih, Dong Ho
林伯勳
Lin, Frank關鍵詞 線性三對角方程組
超立方體網路
平行演算法
Linear Tridiagonal System
hypercube network
parallel algorithm日期 1993 上傳時間 29-Apr-2016 16:32:39 (UTC+8) 摘要 本論文對線性三對角方程組之解法提出平行演算法於超立方體網路 ( 參考文獻 (1) A. H. Samen and D. J. Kuck, A parallel QR algorithm for symmetric tridiagonal matrices, IEEE Trans. Comp. Vol c-26(2), (1977):147-155. (2) Buzbee B. L., Golub G. H., and Nielson C. W., On direct methods for solving poisson’s equations, SIAM J. Number. Anal. 7, 4(dec, 1970): 627-656. (3) C. D. Thompson, Area-time complexity for VLSI, Proc. Of the llth ACM symposium on the theory of computing, ACM, (1979):81-88. (4) C. D. Thompson, A complexity theory for VLSI, Technical Report, Dept. Of computer science, Carnegie-Mellon University, Pittsburgh, pA,,1980. (5) Ferng-Ching Lin and Kuo-Liang Chung, A cost-optimal parallel tridiagonal system solver, Parallel Computing 15 (1990)189-199. (6) Ferng-Ching Lin, Kuo-Liang Chung and Yeong-Nan Yeh, A linear recurrence solver, Proceedings of International Computer Symposium (1990) December 17-19, Hsinchu, Taiwan, R.O.C. (7) M. J. Flynn, Very high-speed computing systems, proc. Of the IEEE 12:1901-1909 (1966) (8) G.H. Golub and C. F. Van Loan, Matrix Computations (North Oxford Academic, Oxford, 1983) (9) H. H. Wang , A parallel method for tridiagonal equations, ACM Trans. Math. Software 7(2) (1981):170-283. (10) H. S. Stone, parallel tridiagonal equation solvers, ACM Trans. Math. Software, 1, NO.4,(1975):289-307. (11) Programming, vol 16, No.2 (1987):127-136. (12) J. Lambiotte and R. Voigt, The solution of tridiagonal linear systems on the CDC STAR-100 computer, ACM Trans. Math. Software.,1, 4(Dec. 1975):308-329. (13) S. A. Browning, The tree machine : A highly concurrent computing environment, Technical Report, (1980):TR:3760, Computer science, California Institute of Technology, Passdena, CA, January, 1980. (14) S. Lakshmivarahan and Sudarshan K. Dhall, Analysis and Design of Parallel Algorithms, (MacGraw-Hill Publishing Company, New York, International edition, 1990) (15) SANJAY RANKA and SARTAJ SAHNI, odd Even Shifts in SIMD Hypercubes, IEEE TRANS. Parallel and distributed systems, vol. 1, No.1, Jan(1990) (16) C. L. Seitz, The cosmic cube, CACM(1984) (17) P. N. Swarztrauber, A parallel algorithm for solving general tridiagonal equations, Math. Comp., vol. 33. (1979):185-199. 描述 碩士
國立政治大學
應用數學系
G795808資料來源 http://thesis.lib.nccu.edu.tw/record/#B2002004243 資料類型 thesis dc.contributor.advisor 施東河 zh_TW dc.contributor.advisor Shih, Dong Ho en_US dc.contributor.author (Authors) 林伯勳 zh_TW dc.contributor.author (Authors) Lin, Frank en_US dc.creator (作者) 林伯勳 zh_TW dc.creator (作者) Lin, Frank en_US dc.date (日期) 1993 en_US dc.date.accessioned 29-Apr-2016 16:32:39 (UTC+8) - dc.date.available 29-Apr-2016 16:32:39 (UTC+8) - dc.date.issued (上傳時間) 29-Apr-2016 16:32:39 (UTC+8) - dc.identifier (Other Identifiers) B2002004243 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/88745 - dc.description (描述) 碩士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 應用數學系 zh_TW dc.description (描述) G795808 zh_TW dc.description.abstract (摘要) 本論文對線性三對角方程組之解法提出平行演算法於超立方體網路 ( zh_TW dc.description.tableofcontents 第一章 簡介﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒2 第二章 循環消減法之平行演算法 2﹒1 方法介紹﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒6 2﹒2 循環消減法之平行演算法於超立方體網路﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒10 2﹒3 循環消減法之平行演算法於縮減之超立方體網路﹒﹒﹒﹒﹒﹒﹒﹒﹒16 2﹒4 費用最佳化及時間分析﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒19 第三章 高斯消去法之平行演算法 3﹒1 方法介紹﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒21 3﹒2 計算尾數值﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒25 3﹒3 三階演算法(Three-phase algorithm)於縮減之超立方體網路﹒﹒﹒﹒﹒﹒28 3﹒4 費用最佳化及時間分析﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒32 第四章 結論﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒33 參考文獻﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒34 zh_TW dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#B2002004243 en_US dc.subject (關鍵詞) 線性三對角方程組 zh_TW dc.subject (關鍵詞) 超立方體網路 zh_TW dc.subject (關鍵詞) 平行演算法 zh_TW dc.subject (關鍵詞) Linear Tridiagonal System en_US dc.subject (關鍵詞) hypercube network en_US dc.subject (關鍵詞) parallel algorithm en_US dc.title (題名) 線性三對角方程組之平行解法 zh_TW dc.title (題名) Parallel Algorithm for Linear Tridiagonal System Solver en_US dc.type (資料類型) thesis en_US dc.relation.reference (參考文獻) (1) A. H. Samen and D. J. Kuck, A parallel QR algorithm for symmetric tridiagonal matrices, IEEE Trans. Comp. Vol c-26(2), (1977):147-155. (2) Buzbee B. L., Golub G. H., and Nielson C. W., On direct methods for solving poisson’s equations, SIAM J. Number. Anal. 7, 4(dec, 1970): 627-656. (3) C. D. Thompson, Area-time complexity for VLSI, Proc. Of the llth ACM symposium on the theory of computing, ACM, (1979):81-88. (4) C. D. Thompson, A complexity theory for VLSI, Technical Report, Dept. Of computer science, Carnegie-Mellon University, Pittsburgh, pA,,1980. (5) Ferng-Ching Lin and Kuo-Liang Chung, A cost-optimal parallel tridiagonal system solver, Parallel Computing 15 (1990)189-199. (6) Ferng-Ching Lin, Kuo-Liang Chung and Yeong-Nan Yeh, A linear recurrence solver, Proceedings of International Computer Symposium (1990) December 17-19, Hsinchu, Taiwan, R.O.C. (7) M. J. Flynn, Very high-speed computing systems, proc. Of the IEEE 12:1901-1909 (1966) (8) G.H. Golub and C. F. Van Loan, Matrix Computations (North Oxford Academic, Oxford, 1983) (9) H. H. Wang , A parallel method for tridiagonal equations, ACM Trans. Math. Software 7(2) (1981):170-283. (10) H. S. Stone, parallel tridiagonal equation solvers, ACM Trans. Math. Software, 1, NO.4,(1975):289-307. (11) Programming, vol 16, No.2 (1987):127-136. (12) J. Lambiotte and R. Voigt, The solution of tridiagonal linear systems on the CDC STAR-100 computer, ACM Trans. Math. Software.,1, 4(Dec. 1975):308-329. (13) S. A. Browning, The tree machine : A highly concurrent computing environment, Technical Report, (1980):TR:3760, Computer science, California Institute of Technology, Passdena, CA, January, 1980. (14) S. Lakshmivarahan and Sudarshan K. Dhall, Analysis and Design of Parallel Algorithms, (MacGraw-Hill Publishing Company, New York, International edition, 1990) (15) SANJAY RANKA and SARTAJ SAHNI, odd Even Shifts in SIMD Hypercubes, IEEE TRANS. Parallel and distributed systems, vol. 1, No.1, Jan(1990) (16) C. L. Seitz, The cosmic cube, CACM(1984) (17) P. N. Swarztrauber, A parallel algorithm for solving general tridiagonal equations, Math. Comp., vol. 33. (1979):185-199. zh_TW
