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Volumn 24, Issue 1-2, 2000, Pages 59-81

New formulas for approximation of π and other transcendental numbers

Author keywords

Algorithms; Digits; Iteration functions; Order of convergence;

Indexed keywords


EID: 0034416248     PISSN: 10171398     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1019184908442     Document Type: Article
Times cited : (4)

References (24)
  • 2
    • 84966222419 scopus 로고
    • The computation of Pi to 29,360,000 decimal digits using Borwein's quadratically convergent algorithm
    • D.H. Bailey, The computation of Pi to 29,360,000 decimal digits using Borwein's quadratically convergent algorithm, Math. Comp. (1988) 283-296.
    • (1988) Math. Comp. , pp. 283-296
    • Bailey, D.H.1
  • 4
    • 0038217783 scopus 로고
    • St. Martin's Press, New York
    • P. Beckmann, History of π (St. Martin's Press, New York, 1971).
    • (1971) History of Π
    • Beckmann, P.1
  • 7
    • 0000608155 scopus 로고
    • Ramanujan, modular equations, and approximation to π, or how to compute one billion digits of π
    • J.M. Borwein, P.B. Borwein and H. Bailey, Ramanujan, modular equations, and approximation to π, or how to compute one billion digits of π, Amer. Math. Monthly (1989) 201-219.
    • (1989) Amer. Math. Monthly , pp. 201-219
    • Borwein, J.M.1    Borwein, P.B.2    Bailey, H.3
  • 8
    • 0016939583 scopus 로고
    • Fast multiple-precision evaluation of elementary functions
    • R.P. Brent, Fast multiple-precision evaluation of elementary functions, J. Assoc. Comput. Mach. 23 (1976) 242-251.
    • (1976) J. Assoc. Comput. Mach. , vol.23 , pp. 242-251
    • Brent, R.P.1
  • 10
    • 0022011265 scopus 로고
    • An efficient formula for linear recurrences
    • C.M. Fiduccia, An efficient formula for linear recurrences, SIAM J. Comput. 14 (1985) 106-112.
    • (1985) SIAM J. Comput. , vol.14 , pp. 106-112
    • Fiduccia, C.M.1
  • 11
    • 0001050260 scopus 로고
    • A new, exact, and easy method of finding roots of any equations generally, and that without any previous reduction
    • E. Halley, A new, exact, and easy method of finding roots of any equations generally, and that without any previous reduction, Philos. Trans. Roy. Soc. London 18 (1694) 136-145.
    • (1694) Philos. Trans. Roy. Soc. London , vol.18 , pp. 136-145
    • Halley, E.1
  • 12
    • 0001295137 scopus 로고    scopus 로고
    • High order iterative methods for approximating square roots
    • B. Kalantari and I. Kalantari, High order iterative methods for approximating square roots, BIT 36 (1996) 395-399.
    • (1996) BIT , vol.36 , pp. 395-399
    • Kalantari, B.1    Kalantari, I.2
  • 13
    • 0031554218 scopus 로고    scopus 로고
    • A basic family of iteration functions for polynomial root finding and its characterizations
    • B. Kalantari, I. Kalantari and R. Zaare-Nahandi, A basic family of iteration functions for polynomial root finding and its characterizations, J. Comput. Appl. Math. 80 (1997) 209-226.
    • (1997) J. Comput. Appl. Math. , vol.80 , pp. 209-226
    • Kalantari, B.1    Kalantari, I.2    Zaare-Nahandi, R.3
  • 14
    • 0004967376 scopus 로고    scopus 로고
    • On the order of a determinantal family of root-finding methods
    • B. Kalantari, On the order of a determinantal family of root-finding methods, BIT 39 (1999) 96-109.
    • (1999) BIT , vol.39 , pp. 96-109
    • Kalantari, B.1
  • 15
    • 0039531837 scopus 로고    scopus 로고
    • Generalization of Taylor's theorem and Newton's method via a new family of determinantal interpolation formulas
    • Technical Report DCS-TR 328, Department of Computer Science, Rutgers University, New Brunswick, NJ
    • B. Kalantari, Generalization of Taylor's theorem and Newton's method via a new family of determinantal interpolation formulas, Technical Report DCS-TR 328, Department of Computer Science, Rutgers University, New Brunswick, NJ (1997), to appear in J. Comput. Appl. Math.
    • (1997) J. Comput. Appl. Math.
    • Kalantari, B.1
  • 16
    • 0043107202 scopus 로고    scopus 로고
    • Technical Report DCS-TR 330, Department of Computer Science, Rutgers University, New Brunswick, NJ
    • B. Kalantar, A lower bound on determinants from linear programming, Technical Report DCS-TR 330, Department of Computer Science, Rutgers University, New Brunswick, NJ (1997).
    • (1997) A Lower Bound on Determinants from Linear Programming
    • Kalantar, B.1
  • 19
    • 0043107201 scopus 로고    scopus 로고
    • Newton's method and generation of a determinantal family of iteration functions
    • Technical Report DCS-TR 371, Department of Computer Science, Rutgers University, New Brunswick, NJ
    • B. Kalantari and J. Gerlach, Newton's method and generation of a determinantal family of iteration functions, Technical Report DCS-TR 371, Department of Computer Science, Rutgers University, New Brunswick, NJ (1998), to appear in J. Comput. Appl. Math.
    • (1998) J. Comput. Appl. Math.
    • Kalantari, B.1    Gerlach, J.2
  • 20
    • 0042105377 scopus 로고    scopus 로고
    • A computational comparison of the first nine members of a determinantal family of rootfinding methods
    • Technical Report DCS-TR 375, Department of Computer Science, Rutgers University, New Brunswick, NJ
    • B. Kalantari and S. Park, A computational comparison of the first nine members of a determinantal family of rootfinding methods, Technical Report DCS-TR 375, Department of Computer Science, Rutgers University, New Brunswick, NJ (1998), to appear in J. Comput. Appl. Math.
    • (1998) J. Comput. Appl. Math.
    • Kalantari, B.1    Park, S.2
  • 22
    • 84966204708 scopus 로고
    • Computation of Pi using Arithmetic-geometric mean
    • E. Salamin, Computation of Pi using Arithmetic-geometric mean, Math. Comp. 30 (1976) 565-570.
    • (1976) Math. Comp. , vol.30 , pp. 565-570
    • Salamin, E.1
  • 23
    • 14944351893 scopus 로고
    • On the geometry of Halley's method
    • T.R. Scavo and J.B. Thoo, On the geometry of Halley's method, Amer. Math. Monthly 102 (1995) 417-426.
    • (1995) Amer. Math. Monthly , vol.102 , pp. 417-426
    • Scavo, T.R.1    Thoo, J.B.2
  • 24
    • 0042105378 scopus 로고    scopus 로고
    • Calculation of π to 51.5 billion decimal digits on distributed memory parallel processors
    • D. Takahashi and Y. Kanada, Calculation of π to 51.5 billion decimal digits on distributed memory parallel processors (in Japanese) Trans. Inform. Process. Soc. Japan 39 (1998) 2074-2083.
    • (1998) Trans. Inform. Process. Soc. Japan , vol.39 , pp. 2074-2083
    • Takahashi, D.1    Kanada, Y.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.