메뉴 건너뛰기




Volumn 37, Issue 3, 2010, Pages

Algorithm 908: Online exact summation of floating-point streams

Author keywords

Floating point summation; Rounding error

Indexed keywords

CONDITION NUMBERS; FLOATING POINT NUMBERS; FLOATING-POINT SUMMATION; INPUT STREAMS; INSTRUCTION LEVEL PARALLELISM; MEMORY EFFICIENT; ON-LINE ALGORITHMS; PROOF OF CORRECTNESS; ROUNDING ERRORS; SUMMANDS;

EID: 77957571319     PISSN: 00983500     EISSN: 15577295     Source Type: Journal    
DOI: 10.1145/1824801.1824815     Document Type: Article
Times cited : (27)

References (24)
  • 1
    • 0033294958 scopus 로고    scopus 로고
    • A distillation algorithm for floating-point summation
    • ANDERSON, I. J. 1999. A distillation algorithm for floating-point summation. SIAMJ. Sci. Comput. 20, 5, 1797-1806.
    • (1999) SIAMJ. Sci. Comput. , vol.20 , Issue.5 , pp. 1797-1806
    • Anderson, I.J.1
  • 2
    • 33846349887 scopus 로고
    • A hierarchical o(nlog n) force-calculation algorithm
    • BARNES, J. AND HUT, P. 1986. A hierarchical o(nlog n) force-calculation algorithm. Nature 324, 446-449.
    • (1986) Nature , vol.324 , pp. 446-449
    • Barnes, J.1    Hut, P.2
  • 4
    • 0000810983 scopus 로고
    • A floating-point technique for extending the available precision
    • DEKKER, T. J. 1971. A floating-point technique for extending the available precision. Numer.Math. 18, 224-242.
    • (1971) Numer. Math. , vol.18 , pp. 224-242
    • Dekker, T.J.1
  • 5
    • 4043118275 scopus 로고    scopus 로고
    • Accurate and efficient floating point summation
    • DEMMEL, J. AND HIDA, Y. 2003. Accurate and efficient floating point summation. SIAM J. Sci. Comput. 25, 1214-1248.
    • (2003) SIAM J. Sci. Comput. , vol.25 , pp. 1214-1248
    • Demmel, J.1    Hida, Y.2
  • 6
    • 0000813940 scopus 로고    scopus 로고
    • A parallel tree code
    • DUBINSKI, J. 1996. A parallel tree code. New Astron. 1, 133-147.
    • (1996) New Astron. , vol.1 , pp. 133-147
    • Dubinski, J.1
  • 9
    • 14844300898 scopus 로고    scopus 로고
    • A survey of shadowing methods for numerical solutions of ordinary differential equations
    • HAYES, W. B. 2005. A survey of shadowing methods for numerical solutions of ordinary differential equations. Appl. Numer. Math. 53, 2-4, 299-321.
    • (2005) Appl. Numer. Math. , vol.53 , Issue.2-4 , pp. 299-321
    • Hayes, W.B.1
  • 10
    • 0000155361 scopus 로고
    • The accuracy of floating point summation
    • HIGHAM, N. J. 1993. The accuracy of floating point summation. SIAM J. Sci. Comput. 14, 4, 783-799.
    • (1993) SIAM J. Sci. Comput. , vol.14 , Issue.4 , pp. 783-799
    • Higham, N.J.1
  • 12
    • 0002445594 scopus 로고
    • LSODE and LSODI, two new initial value ordinary differential equation solvers
    • HINDMARSH, A. C. 1980. LSODE and LSODI, two new initial value ordinary differential equation solvers. ACM-SIGNUM Newslett. 15, 4, 10-11.
    • (1980) ACM-SIGNUM Newslett. , vol.15 , Issue.4 , pp. 10-11
    • Hindmarsh, A.C.1
  • 13
    • 0010218629 scopus 로고
    • A tree code with logarithmic reduction of force terms, hierarchical regularization of all variables, and explicit accuracy controls
    • JERNIGAN, J. G. AND PORTER, D. H. 1989. A tree code with logarithmic reduction of force terms, hierarchical regularization of all variables, and explicit accuracy controls. Astrophys. J. Suppl. Series 71, 871-893.
    • (1989) Astrophys. J. Suppl. Series , vol.71 , pp. 871-893
    • Jernigan, J.G.1    Porter, D.H.2
  • 14
    • 0003657590 scopus 로고    scopus 로고
    • 3rd Ed., SeminumericalAlgorithms. Addison-Wesley, Reading, MA
    • KNUTH, D. E. 1998. The Art of Computer Programming, 3rd Ed. Vol.2 SeminumericalAlgorithms. Addison-Wesley, Reading, MA.
    • (1998) The Art of Computer Programming , vol.2
    • Knuth, D.E.1
  • 15
    • 0016892284 scopus 로고
    • Formalization and implementation of floating-point matrix operations
    • KULISCH, U. AND BOHLENDER, G. 1976. Formalization and implementation of floating-point matrix operations. Comput. 16, 239-261.
    • (1976) Comput. , vol.16 , pp. 239-261
    • Kulisch, U.1    Bohlender, G.2
  • 18
    • 77956237657 scopus 로고    scopus 로고
    • Ultimately fast accurate summation
    • RUMP, S. M. 2009. Ultimately fast accurate summation. SIAM J. Sci. Comput. 31, 5, 3446-3502.
    • (2009) SIAM J. Sci. Comput. , vol.31 , Issue.5 , pp. 3446-3502
    • Rump, S.M.1
  • 19
    • 55049129860 scopus 로고    scopus 로고
    • Accurate floating-point summation Part I: Faithful rounding
    • RUMP, S. M., OGITA, T., AND OISHI, S. 2008a. Accurate floating-point summation Part I: Faithful rounding. SIAM J. Sci. Comput. 31, 189-224.
    • (2008) SIAM J. Sci. Comput. , vol.31 , pp. 189-224
    • Rump, S.M.1    Ogita, T.2    Oishi, S.3
  • 20
    • 67649610606 scopus 로고    scopus 로고
    • Accurate floating-point summation Part II: Sign, k-fold faithful and rounding to nearest
    • RUMP, S. M., OGITA, T., AND OISHI, S. 2008b. Accurate floating-point summation Part II: Sign, k-fold faithful and rounding to nearest. SIAM J. Sci. Comput. 31, 1269-1302.
    • (2008) SIAM J. Sci. Comput. , vol.31 , pp. 1269-1302
    • Rump, S.M.1    Ogita, T.2    Oishi, S.3
  • 22
    • 67649606341 scopus 로고    scopus 로고
    • Fast, guaranteed-accurate sums of many floating-point numbers
    • G. Hanrot and P. Zimmermann Eds., INRIA, France
    • ZHU, Y.-K. AND HAYES, W. B. 2006. Fast, guaranteed-accurate sums of many floating-point numbers. In Proceedings of the 7th Real Numbers and Computers Conference, G. Hanrot and P. Zimmermann Eds., INRIA, France, 11-22.
    • (2006) Proceedings of the 7th Real Numbers and Computers Conference , pp. 11-22
    • Zhu, Y.-K.1    Hayes, W.B.2
  • 23
    • 77957557605 scopus 로고    scopus 로고
    • Correct rounding and a hybrid approach to exact floating-point summation
    • ZHU, Y.-K. AND HAYES, W. B. 2009. Correct rounding and a hybrid approach to exact floating-point summation. SIAM J. Sci. Comput. 31, 2981-3001.
    • (2009) SIAM J. Sci. Comput. , vol.31 , pp. 2981-3001
    • Zhu, Y.-K.1    Hayes, W.B.2
  • 24
    • 24644433724 scopus 로고    scopus 로고
    • A new distillation algorithm for floating-point summation
    • ZHU, Y.-K., YONG, J.-H., AND ZHENG, G.-Q. 2005. A new distillation algorithm for floating-point summation. SIAM J. Sci. Comput. 26, 2066-2078.
    • (2005) SIAM J. Sci. Comput. , vol.26 , pp. 2066-2078
    • Zhu, Y.-K.1    Yong, J.-H.2    Zheng, G.-Q.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.