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Volumn 121, Issue 3, 2012, Pages 473-502

Quasi-Monte Carlo rules for numerical integration over the unit sphere S 2

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EID: 84862263339     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00211-011-0444-6     Document Type: Article
Times cited : (30)

References (45)
  • 4
    • 84974189036 scopus 로고
    • Sums of distances between points on a sphere-an application of the theory of irregularities of distribution to discrete geometry
    • Beck J.: Sums of distances between points on a sphere-an application of the theory of irregularities of distribution to discrete geometry. Mathematika 31(1), 33-41 (1984).
    • (1984) Mathematika , vol.31 , Issue.1 , pp. 33-41
    • Beck, J.1
  • 7
    • 37649012908 scopus 로고    scopus 로고
    • Asymptotics for discrete weighted minimal Riesz energy problems on rectifiable sets
    • (electronic)
    • Borodachov S. V., Hardin D. P., Saff E. B.: Asymptotics for discrete weighted minimal Riesz energy problems on rectifiable sets. Trans. Am. Math. Soc. 360(3), 1559-1580 (2008) (electronic).
    • (2008) Trans. Am. Math. Soc. , vol.360 , Issue.3 , pp. 1559-1580
    • Borodachov, S.V.1    Hardin, D.P.2    Saff, E.B.3
  • 8
    • 0023979638 scopus 로고
    • Algorithm 659: Implementing sobol's quasirandom sequence generator
    • Bratley P., Fox B. L.: Algorithm 659: Implementing sobol's quasirandom sequence generator. ACM Trans. Math. Softw. 14, 88-100 (1988).
    • (1988) ACM Trans. Math. Softw. , vol.14 , pp. 88-100
    • Bratley, P.1    Fox, B.L.2
  • 9
    • 47249116205 scopus 로고    scopus 로고
    • Optimal logarithmic energy points on the unit sphere
    • Brauchart J. S.: Optimal logarithmic energy points on the unit sphere. Math. Comp. 77(263), 1599-1613 (2008).
    • (2008) Math. Comp. , vol.77 , Issue.263 , pp. 1599-1613
    • Brauchart, J.S.1
  • 12
    • 34250831282 scopus 로고    scopus 로고
    • Universally optimal distribution of points on spheres
    • (electronic)
    • Cohn H., Kumar A.: Universally optimal distribution of points on spheres. J. Am. Math. Soc. 20(1), 99-148 (2007) (electronic).
    • (2007) J. Am. Math. Soc. , vol.20 , Issue.1 , pp. 99-148
    • Cohn, H.1    Kumar, A.2
  • 13
    • 0031082707 scopus 로고    scopus 로고
    • Equidistribution on the sphere
    • Cui J., Freeden W.: Equidistribution on the sphere. SIAM J. Sci. Comput. 18(2), 595-609 (1997).
    • (1997) SIAM J. Sci. Comput. , vol.18 , Issue.2 , pp. 595-609
    • Cui, J.1    Freeden, W.2
  • 14
    • 84862264974 scopus 로고    scopus 로고
    • A best possible upper bound on the star discrepancy of (t, m, 2)-nets
    • Dick J., Kritzer P.: A best possible upper bound on the star discrepancy of (t, m, 2)-nets. Monte Carlo Methods Appl. 12(1), 1-17 (2006).
    • (2006) Monte Carlo Methods Appl. , vol.12 , Issue.1 , pp. 1-17
    • Dick, J.1    Kritzer, P.2
  • 16
    • 0346894538 scopus 로고
    • On a problem in the theory of uniform distribution
    • (Indagationes Math. 10, 370-378, 1948)
    • Erdös, P., Turán, P.: On a problem in the theory of uniform distribution. I. Nederl. Akad. Wetensch., Proc. 51, 1146-1154 (Indagationes Math. 10, 370-378, 1948) (1948).
    • (1948) I. Nederl. Akad. Wetensch., Proc , vol.51 , pp. 1146-1154
    • Erdös, P.1    Turán, P.2
  • 17
    • 0346894538 scopus 로고
    • On a problem in the theory of uniform distribution. II
    • (Indagationes Math. 10, 406-413, 1948)
    • Erdös, P., Turán, P.: On a problem in the theory of uniform distribution. II. Nederl. Akad. Wetensch., Proc. 51, 1262-1269 (Indagationes Math. 10, 406-413, 1948) (1948).
    • (1948) Nederl. Akad. Wetensch., Proc , vol.51 , pp. 1262-1269
    • Erdös, P.1    Turán, P.2
  • 18
    • 0001013260 scopus 로고
    • Discrépance de suites associées àà un système de numération (en dimension s)
    • Faure H.: Discrépance de suites associées àà un système de numération (en dimension s). Acta Arith. 41(4), 337-351 (1982).
    • (1982) Acta Arith. , vol.41 , Issue.4 , pp. 337-351
    • Faure, H.1
  • 19
    • 0011265052 scopus 로고
    • Erdo{double acute}s-Turán type discrepancy bounds
    • Grabner P. J.: Erdo{double acute}s-Turán type discrepancy bounds. Monatsh. Math. 111(2), 127-135 (1991).
    • (1991) Monatsh. Math. , vol.111 , Issue.2 , pp. 127-135
    • Grabner, P.J.1
  • 20
    • 27844497928 scopus 로고    scopus 로고
    • Discretizing manifolds via minimum energy points
    • Hardin D. P., Saff E. B.: Discretizing manifolds via minimum energy points. Not. Am. Math. Soc. 51(10), 1186-1194 (2004).
    • (2004) Not. Am. Math. Soc. , vol.51 , Issue.10 , pp. 1186-1194
    • Hardin, D.P.1    Saff, E.B.2
  • 21
    • 13844275746 scopus 로고    scopus 로고
    • Minimal Riesz energy point configurations for rectifiable d-dimensional manifolds
    • Hardin D. P., Saff E. B.: Minimal Riesz energy point configurations for rectifiable d-dimensional manifolds. Adv. Math. 193(1), 174-204 (2005).
    • (2005) Adv. Math. , vol.193 , Issue.1 , pp. 174-204
    • Hardin, D.P.1    Saff, E.B.2
  • 23
    • 10844292762 scopus 로고    scopus 로고
    • Remark on algorithm 659: Implementing sobol′s quasirandom sequence generator
    • Joe S., Kuo F. Y.: Remark on algorithm 659: Implementing sobol′s quasirandom sequence generator. ACM Trans. Math. Softw. 29, 49-57 (2003).
    • (2003) ACM Trans. Math. Softw. , vol.29 , pp. 49-57
    • Joe, S.1    Kuo, F.Y.2
  • 24
    • 33646877546 scopus 로고
    • An inequality connected with Weyl's criterion for uniform distribution
    • Amer. Math. Soc., Providence, R. I
    • LeVeque, W. J.: An inequality connected with Weyl's criterion for uniform distribution. In: Proc. Sympos. Pure Math., vol. VIII, pp. 22-30. Amer. Math. Soc., Providence, R. I. (1965).
    • (1965) Proc. Sympos. Pure Math. , vol.VIII , pp. 22-30
    • LeVeque, W.J.1
  • 25
    • 0347174830 scopus 로고    scopus 로고
    • Some trigonometric extremal functions and the Erdo{double acute}s-Turán type inequalities
    • Li X.-J., Vaaler J. D.: Some trigonometric extremal functions and the Erdo{double acute}s-Turán type inequalities. Indiana Univ. Math. J. 48(1), 183-236 (1999).
    • (1999) Indiana Univ. Math. J. , vol.48 , Issue.1 , pp. 183-236
    • Li, X.-J.1    Vaaler, J.D.2
  • 26
    • 84990604340 scopus 로고
    • Hecke operators and distributing points on the sphere
    • [Frontiers of the mathematical sciences: 1985 (New York, 1985)]
    • Lubotzky, A., Phillips, R., Sarnak, P.: Hecke operators and distributing points on the sphere. I. Commun. Pure Appl. Math., 39(suppl.): S149-S186, 1986 [Frontiers of the mathematical sciences: 1985 (New York, 1985)].
    • (1986) I. Commun. Pure Appl. Math. , vol.39 , Issue.SUPPL.
    • Lubotzky, A.1    Phillips, R.2    Sarnak, P.3
  • 27
    • 0000382131 scopus 로고    scopus 로고
    • 2-discrepancy for anchored boxes
    • 2-discrepancy for anchored boxes. J. Complex. 14(4), 527-556 (1998).
    • (1998) J. Complex. , vol.14 , Issue.4 , pp. 527-556
    • Matoušek, J.1
  • 29
    • 77952671977 scopus 로고    scopus 로고
    • Leveque type inequalities and discrepancy estimates for minimal energy configurations on spheres
    • Narcowich F. J., Sun X., Ward J. D., Wu Z.: Leveque type inequalities and discrepancy estimates for minimal energy configurations on spheres. J. Approx. Theory 162(6), 1256-1278 (2010).
    • (2010) J. Approx. Theory , vol.162 , Issue.6 , pp. 1256-1278
    • Narcowich, F.J.1    Sun, X.2    Ward, J.D.3    Wu, Z.4
  • 30
    • 0002071152 scopus 로고
    • Low-discrepancy and low-dispersion sequences
    • Niederreiter H.: Low-discrepancy and low-dispersion sequences. J. Number Theory 30(1), 51-70 (1988).
    • (1988) J. Number Theory , vol.30 , Issue.1 , pp. 51-70
    • Niederreiter, H.1
  • 31
    • 0003244922 scopus 로고
    • Random number generation and quasi-Monte Carlo methods
    • Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA
    • Niederreiter, H.: Random number generation and quasi-Monte Carlo methods. In: CBMS-NSF Regional Conference Series in Applied Mathematics, vol 63. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA (1992).
    • (1992) CBMS-NSF Regional Conference Series in Applied Mathematicsz , vol.63
    • Niederreiter, H.1
  • 32
    • 0030194541 scopus 로고    scopus 로고
    • Low-discrepancy sequences and global function fields with many rational places
    • Niederreiter H., Xing C.: Low-discrepancy sequences and global function fields with many rational places. Finite Fields Appl. 2(3), 241-273 (1996).
    • (1996) Finite Fields Appl. , vol.2 , Issue.3 , pp. 241-273
    • Niederreiter, H.1    Xing, C.2
  • 33
    • 21844523415 scopus 로고
    • Low-discrepancy sequences obtained from algebraic function fields over finite fields
    • Niederreiter H., Xing C. P.: Low-discrepancy sequences obtained from algebraic function fields over finite fields. Acta Arith. 72(3), 281-298 (1995).
    • (1995) Acta Arith. , vol.72 , Issue.3 , pp. 281-298
    • Niederreiter, H.1    Xing, C.P.2
  • 34
    • 4243059534 scopus 로고    scopus 로고
    • Variance with alternative scramblings of digital nets
    • Owen A. B.: Variance with alternative scramblings of digital nets. ACM Trans. Model. Comput. Simul. 12, 363-378 (2003).
    • (2003) ACM Trans. Model. Comput. Simul. , vol.12 , pp. 363-378
    • Owen, A.B.1
  • 35
    • 0002851522 scopus 로고
    • On irregularities of distribution
    • Roth K. F.: On irregularities of distribution. Mathematika 1, 73-79 (1954).
    • (1954) Mathematika , vol.1 , pp. 73-79
    • Roth, K.F.1
  • 36
    • 0002462777 scopus 로고
    • Irregularities of distribution. IV
    • Schmidt W. M.: Irregularities of distribution. IV. Invent. Math. 7, 55-82 (1969).
    • (1969) Invent. Math. , vol.7 , pp. 55-82
    • Schmidt, W.M.1
  • 37
    • 0002278399 scopus 로고
    • Estimates of mass distributions from their potentials and energies
    • Sjögren P.: Estimates of mass distributions from their potentials and energies. Ark. Mat. 10, 59-77 (1972).
    • (1972) Ark. Mat. , vol.10 , pp. 59-77
    • Sjögren, P.1
  • 38
    • 4043098361 scopus 로고    scopus 로고
    • Extremal systems of points and numerical integration on the sphere
    • Sloan I. H., Womersley R. S.: Extremal systems of points and numerical integration on the sphere. Adv. Comput. Math. 21(1-2), 107-125 (2004).
    • (2004) Adv. Comput. Math. , vol.21 , Issue.1-2 , pp. 107-125
    • Sloan, I.H.1    Womersley, R.S.2
  • 39
    • 0001352321 scopus 로고
    • Distribution of points in a cube and approximate evaluation of integrals
    • Soboĺ I. M.: Distribution of points in a cube and approximate evaluation of integrals. Ž Vyčisl. Mat. i Mat. Fiz. 7, 784-802 (1967).
    • (1967) ŽVyčisl. Mat. I Mat. Fiz. , vol.7 , pp. 784-802
    • Soboĺ, I.M.1
  • 40
    • 84968518878 scopus 로고
    • Sums of distances between points on a sphere. II
    • Stolarsky K. B.: Sums of distances between points on a sphere. II. Proc. Am. Math. Soc. 41, 575-582 (1973).
    • (1973) Proc. Am. Math. Soc. , vol.41 , pp. 575-582
    • Stolarsky, K.B.1
  • 41
    • 41549086984 scopus 로고    scopus 로고
    • Spherical basis functions and uniform distribution of points on spheres
    • Sun X., Chen Z.: Spherical basis functions and uniform distribution of points on spheres. J. Approx. Theory 151(2), 186-207 (2008).
    • (2008) J. Approx. Theory , vol.151 , Issue.2 , pp. 186-207
    • Sun, X.1    Chen, Z.2
  • 42
    • 84973998293 scopus 로고
    • On means of distances on the surface of a sphere (lower bounds)
    • Wagner G.: On means of distances on the surface of a sphere (lower bounds). Pac. J. Math. 144(2), 389-398 (1990).
    • (1990) Pac. J. Math. , vol.144 , Issue.2 , pp. 389-398
    • Wagner, G.1
  • 43
    • 1542638369 scopus 로고
    • Erdo{double acute}s-Turán inequalities for distance functions on spheres
    • Wagner G.: Erdo{double acute}s-Turán inequalities for distance functions on spheres. Michigan Math. J. 39(1), 17-34 (1992).
    • (1992) Michigan Math. J. , vol.39 , Issue.1 , pp. 17-34
    • Wagner, G.1
  • 44
    • 84973999972 scopus 로고
    • On means of distances on the surface of a sphere. II. Upper bounds
    • Wagner G.: On means of distances on the surface of a sphere. II. Upper bounds. Pac. J. Math. 154(2), 381-396 (1992).
    • (1992) Pac. J. Math. , vol.154 , Issue.2 , pp. 381-396
    • Wagner, G.1
  • 45
    • 21844527203 scopus 로고
    • A construction of low-discrepancy sequences using global function fields
    • Xing C. P., Niederreiter H.: A construction of low-discrepancy sequences using global function fields. Acta Arith. 73(1), 87-102 (1995).
    • (1995) Acta Arith. , vol.73 , Issue.1 , pp. 87-102
    • Xing, C.P.1    Niederreiter, H.2


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