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Volumn 59, Issue 3, 1997, Pages 223-236

Numerical integration of singular integrands using low-discrepancy sequences

Author keywords

Improper integrals; Quasi Monte Carlo methods

Indexed keywords

ERROR ANALYSIS; FUNCTIONS; INTEGRAL EQUATIONS; MONTE CARLO METHODS; THEOREM PROVING;

EID: 0031332920     PISSN: 0010485X     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02684442     Document Type: Article
Times cited : (8)

References (13)
  • 1
    • 0023979638 scopus 로고
    • Algorithm 659. Implementing Sobol's quasi-random sequence generator
    • Bratley, P., Fox, B. L.: Algorithm 659. Implementing Sobol's quasi-random sequence generator. ACM Trans. Math. Software 14, 88-100 (1988).
    • (1988) ACM Trans. Math. Software , vol.14 , pp. 88-100
    • Bratley, P.1    Fox, B.L.2
  • 3
    • 0039930999 scopus 로고
    • Irregular distribution of {n β}, n = 1,2,3,..., quadrature of singular integrands, and curious hypergeometric series
    • N.S.
    • Driver, K. A., Lubinsky, D. S., Petruska, G., Sarnak, P.: Irregular distribution of {n β}, n = 1,2,3,..., quadrature of singular integrands, and curious hypergeometric series. Indag. Mathem., N.S. 2, 469-481 (1991).
    • (1991) Indag. Mathem. , vol.2 , pp. 469-481
    • Driver, K.A.1    Lubinsky, D.S.2    Petruska, G.3    Sarnak, P.4
  • 4
    • 0002020770 scopus 로고
    • On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals
    • Halton, J. H.: On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals. Numer. Math. 2, 84-90 (1960).
    • (1960) Numer. Math. , vol.2 , pp. 84-90
    • Halton, J.H.1
  • 6
    • 84966218512 scopus 로고
    • Rates of convergence of Gaussian quadrature for singular integrands
    • Lubinsky, D. S., Rabinowitz, P.: Rates of convergence of Gaussian quadrature for singular integrands. Math. Comp. 43, 219-242 (1987)
    • (1987) Math. Comp. , vol.43 , pp. 219-242
    • Lubinsky, D.S.1    Rabinowitz, P.2
  • 7
    • 0000997571 scopus 로고
    • Quasi-Monte Carlo methods and pseudo-random numbers
    • Niederreiter, H.: Quasi-Monte Carlo methods and pseudo-random numbers. Bull. Am. Math. Soc. 84, 957-1041 (1978).
    • (1978) Bull. Am. Math. Soc. , vol.84 , pp. 957-1041
    • Niederreiter, H.1
  • 8
    • 0002071152 scopus 로고
    • Low-discrepancy and low-dispersion sequences
    • Niederreiter, H.: Low-discrepancy and low-dispersion sequences. J. Number Theor. 30, 51-70 (1988).
    • (1988) J. Number Theor. , vol.30 , pp. 51-70
    • Niederreiter, H.1
  • 10
    • 0002307184 scopus 로고    scopus 로고
    • Quasi-Monte Carlo methods for numerical integration - A comparison of different low-discrepancy sequences
    • Radović, I., Sobol', I. M., Tichy, R. F.: Quasi-Monte Carlo methods for numerical integration - a comparison of different low-discrepancy sequences. Monte Carlo Methods Appl. 2, 1-14 (1996).
    • (1996) Monte Carlo Methods Appl. , vol.2 , pp. 1-14
    • Radović, I.1    Sobol', I.M.2    Tichy, R.F.3
  • 11
    • 49949136136 scopus 로고
    • The distribution of points in a cube and the approximate evaluation of integrals
    • Sobol', I. M.: The distribution of points in a cube and the approximate evaluation of integrals. USSR Comput. Math. Phys. 7, 86-112 (1967).
    • (1967) USSR Comput. Math. Phys. , vol.7 , pp. 86-112
    • SoboL', I.M.1
  • 12
    • 0010207218 scopus 로고
    • Calculation of improper integrals using uniformly distributed sequences
    • Sobol', I. M.: Calculation of improper integrals using uniformly distributed sequences. Soviet Math. Dokl. 14, 734-738 (1973).
    • (1973) Soviet Math. Dokl. , vol.14 , pp. 734-738
    • Sobol', I.M.1
  • 13
    • 6244253442 scopus 로고
    • On the use of low-discrepancy sequences for the approximate computation of improper integrals
    • Sobolev, S. L. ed., (in Russian). Novosibirsk: Nauka
    • Sobol', I. M.: On the use of low-discrepancy sequences for the approximate computation of improper integrals. In: Theory of cubature formulas and applications to certain problems in mathematical physics Sobolev, S. L. ed.), pp. 62-66 (in Russian). Novosibirsk: Nauka, 1973.
    • (1973) Theory of Cubature Formulas and Applications to Certain Problems in Mathematical Physics , pp. 62-66
    • Sobol', I.M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.