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Volumn 1, Issue 2-3, 2001, Pages 167-184

Extrapolation Methods for Infinite Multiple Series and Integrals

Author keywords

Convergence acceleration; multi dimenional integrals; multi vibrate extrapolation; multiple series

Indexed keywords

EXTRAPOLATION;

EID: 61849133505     PISSN: 14727978     EISSN: None     Source Type: Journal    
DOI: 10.3233/JCM-2001-12-303     Document Type: Article
Times cited : (5)

References (28)
  • 1
    • 0000007662 scopus 로고
    • Rational approximants defined from double power series
    • J.S.R. Chisholmn. Rational approximants defined from double power series. Math. Gomp., 27:841-848, 1973.
    • (1973) Math. Gomp. , vol.27 , pp. 841-848
    • Chisholmn, J.S.R.1
  • 2
    • 80052260719 scopus 로고
    • Rational approximants defined from power series in ii variables
    • J.S.R. Chisholm and J. McEwan. Rational approximants defined from power series in ii variables. Proc. Roy. Soc. London, A 336:421-452, 1974.
    • (1974) Proc. Roy. Soc. London A , vol.336 , pp. 421-452
    • Chisholm, J.S.R.1    McEwan, J.2
  • 4
    • 0002786366 scopus 로고
    • A multivariate convergence theorem of the de Montessus de Ballore type
    • A. Cuyt. A multivariate convergence theorem of the de Montessus de Ballore type. J. Gomp. Appl. Math., 32:47-57, 1990.
    • (1990) J. Gomp. Appl. Math. , vol.32 , pp. 47-57
    • Cuyt, A.1
  • 5
    • 0001650649 scopus 로고
    • Multivariate partial Newton-Padé and Newton-Padé type approximations
    • A. Cuyt. Multivariate partial Newton-Padé and Newton-Padé type approximations. J. Approx. Theory, 72:301-316, 1993.
    • (1993) J. Approx. Theory , vol.72 , pp. 301-316
    • Cuyt, A.1
  • 6
    • 0023427925 scopus 로고
    • An algorithm for a generalization of the Richardson extrapolation process
    • W.F. Ford and A. Sidi. An algorithm for a generalization of the Richardson extrapolation process. SIAM J. Numer. Anal., 24:1212-1232, 1987.
    • (1987) SIAM J. Numer. Anal. , vol.24 , pp. 1212-1232
    • Ford, W.F.1    Sidi, A.2
  • 8
    • 0032393496 scopus 로고    scopus 로고
    • The d2-transformation for infinite double series and the D2-transformation for infinite double integrals
    • C. Greif and D. Levin. The d2-transformation for infinite double series and the D2-transformation for infinite double integrals. Math. Corap., 67:695-714, 1998.
    • (1998) Math. Corap. , vol.67 , pp. 695-714
    • Greif, C.1    Levin, D.2
  • 9
    • 0013382565 scopus 로고
    • General rational approximants in N variables
    • R. Hughes Jones. General rational approximants in N variables. J. Approx. Theory, 16:201-233, 1976.
    • (1976) J. Approx. Theory , vol.16 , pp. 201-233
    • Hughes Jones, R.1
  • 10
    • 84948301871 scopus 로고
    • Development of non-linear transformations for improving convergence of sequences
    • D. Levin. Development of non-linear transformations for improving convergence of sequences. Intern. J. Computer Math., B3:371-388, 1973.
    • (1973) Intern. J. Computer Math. , vol.B3 , pp. 371-388
    • Levin, D.1
  • 11
    • 0041893267 scopus 로고
    • General order Padé-type rational approximants defined from double power series
    • D. Levin. General order Padé-type rational approximants defined from double power series. J. Inst. Maths. Applics., 18:1-8, 1976.
    • (1976) J. Inst. Maths. Applics. , vol.18 , pp. 1-8
    • Levin, D.1
  • 12
    • 84966211061 scopus 로고
    • On accelerating the convergence of infinite double series and integrals
    • D. Levin. On accelerating the convergence of infinite double series and integrals. Math. Comp., 35:1331-1345, 1980.
    • (1980) Math. Comp. , vol.35 , pp. 1331-1345
    • Levin, D.1
  • 13
    • 0001449239 scopus 로고
    • Two new classes of nonlinear transformations for accelerating the convergence of infinite integrals and series
    • Originally appeared as a Tel Aviv University preprint in 1975
    • D. Levin and A. Sidi. Two new classes of nonlinear transformations for accelerating the convergence of infinite integrals and series. Appl. Math. Cornp., 9:175-215, 1981. Originally appeared as a Tel Aviv University preprint in 1975.
    • (1981) Appl. Math. Cornp. , vol.9 , pp. 175-215
    • Levin, D.1    Sidi, A.2
  • 16
    • 0001293659 scopus 로고
    • Some properties of a generalization of the Richardson extrapolation process
    • A. Sidi. Some properties of a generalization of the Richardson extrapolation process. J. Inst. Maths. Applics. 24:327-346, 1979.
    • (1979) J. Inst. Maths. Applics. , vol.24 , pp. 327-346
    • Sidi, A.1
  • 17
    • 0003054141 scopus 로고
    • Extrapolation methods for oscillatory infinite integrals
    • A. Sidi. Extrapolation methods for oscillatory infinite integrals. J. Inst. Maths. Applies., 26:1-20, 1980.
    • (1980) J. Inst. Maths. Applies. , vol.26 , pp. 1-20
    • Sidi, A.1
  • 18
    • 0001045744 scopus 로고
    • An algorithm for a special case of a generalization of the Richardson extrapolation process
    • A. Sidi. An algorithm for a special case of a generalization of the Richardson extrapolation process. iVuiner. Math., 38:299-307, 1982.
    • (1982) I Vuiner. Math. , vol.38 , pp. 299-307
    • Sidi, A.1
  • 19
    • 84968492712 scopus 로고
    • The numerical evaluation of very oscillatory infinite integrals by extrapolation
    • A. Sidi. The numerical evaluation of very oscillatory infinite integrals by extrapolation. Math. Comp., 38:517-529, 1982.
    • (1982) Math. Comp. , vol.38 , pp. 517-529
    • Sidi, A.1
  • 20
    • 0023287499 scopus 로고
    • Extrapolation methods for divergent oscillatory infinite integrals that are defined in the sense of summability
    • A. Sidi. Extrapolation methods for divergent oscillatory infinite integrals that are defined in the sense of summability. J. Comp. Appl. Math., 17:105-114, 1987.
    • (1987) J. Comp. Appl. Math. , vol.17 , pp. 105-114
    • Sidi, A.1
  • 21
    • 84966245428 scopus 로고
    • A user-friendly extrapolation method for oscillatory infinite integrals
    • A. Sidi. A user-friendly extrapolation method for oscillatory infinite integrals. Math. Comp., 51:249-266, 1988.
    • (1988) Math. Comp. , vol.51 , pp. 249-266
    • Sidi, A.1
  • 22
    • 0000031374 scopus 로고
    • Acceleration of convergence of (generalized) Fourier series by the d-transformation
    • A. Sidi. Acceleration of convergence of (generalized) Fourier series by the d-transformation. Annals Numer. Math., 2:381-406, 1995.
    • (1995) Annals Numer. Math. , vol.2 , pp. 381-406
    • Sidi, A.1
  • 23
    • 21844524846 scopus 로고
    • Convergence analysis for a generalized Richardson extrapolation process with an application to the d(1)transformation on convergent and divergent logarithmic sequences
    • A. Sidi. Convergence analysis for a generalized Richardson extrapolation process with an application to the d(1)transformation on convergent and divergent logarithmic sequences. Math. Comp., 64:1627-1657, 1995.
    • (1995) Math. Comp. , vol.64 , pp. 1627-1657
    • Sidi, A.1
  • 24
    • 0031550485 scopus 로고    scopus 로고
    • Computation of infinite integrals involving Bessel functions of arbitrary order by the D-transformation
    • A. Sidi. Computation of infinite integrals involving Bessel functions of arbitrary order by the D-transformation. J. Gonzp. Appi. Math., 78:125-130, 1997.
    • (1997) J. Gonzp. Appi. Math. , vol.78 , pp. 125-130
    • Sidi, A.1
  • 25
    • 0033343683 scopus 로고    scopus 로고
    • Further convergence and stability results for the generalized Richardson extrapolation process GREP' with an application to the D'-transformation for infinite integrals
    • A. Sidi. Further convergence and stability results for the generalized Richardson extrapolation process GREP' with an application to the D'-transformation for infinite integrals. J. Gomp. Appi. Math., 112:269-290, 1999.
    • (1999) J. Gomp. Appi. Math. , vol.112 , pp. 269-290
    • Sidi, A.1
  • 26
    • 0040281096 scopus 로고
    • Rational approximations from the d-transformation
    • A. Sidi and D. Levin. Rational approximations from the d-transformation. IMA J. Namer. Anal., 2:153-167, 1982.
    • (1982) IMA J. Namer. Anal. , vol.2 , pp. 153-167
    • Sidi, A.1    Levin, D.2
  • 27
    • 0003105647 scopus 로고
    • Acceleration of linear and logarithmic convergence
    • D.A. Smith and W.F. Ford. Acceleration of linear and logarithmic convergence. SIAM J. Namer. Anal., 16:223-240, 1979.
    • (1979) SIAM J. Namer. Anal. , vol.16 , pp. 223-240
    • Smith, D.A.1    Ford, W.F.2
  • 28
    • 84968476219 scopus 로고
    • Numerical comparisons of nonlinear convergence accelerators
    • D.A. Smith and W.F. Ford. Numerical comparisons of nonlinear convergence accelerators. Math. Gomp., 38:481-499, 1982.
    • (1982) Math. Gomp. , vol.38 , pp. 481-499
    • Smith, D.A.1    Ford, W.F.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.