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Volumn 16, Issue 6, 2010, Pages 813-839

On Energy, Discrepancy and Group Invariant Measures on Measurable Subsets of Euclidean Space

Author keywords

Capacity; Cubature; Discrepancy; Distribution; Energy minimizer; Equilibrium measure; Group invariant kernel; Group invariant measure; Numerical integration; Positive definite; Potential field; Reproducing Hilbert space; Riesz kernel; Signed measure

Indexed keywords


EID: 78449269048     PISSN: 10695869     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00041-010-9153-2     Document Type: Article
Times cited : (24)

References (40)
  • 3
    • 33846980427 scopus 로고    scopus 로고
    • On the support of the equilibrium measure for arcs of the unit circle and real intervals
    • Benko, D., Damelin, S. B., Dragnev, P. D.: On the support of the equilibrium measure for arcs of the unit circle and real intervals. Electron. Trans. Numer. Anal. 25, 27-40 (2006).
    • (2006) Electron. Trans. Numer. Anal. , vol.25 , pp. 27-40
    • Benko, D.1    Damelin, S.B.2    Dragnev, P.D.3
  • 4
    • 51249162249 scopus 로고
    • A general discrepancy theorem
    • Blatt, H. P., Mhaskar, H. N.: A general discrepancy theorem. Ark. Mat. 31, 219-246 (1993).
    • (1993) Ark. Mat. , vol.31 , pp. 219-246
    • Blatt, H.P.1    Mhaskar, H.N.2
  • 5
    • 0000272653 scopus 로고
    • Randomization of number theoretic methods for multiple integration
    • Cranley, R., Patterson, T. N. L.: Randomization of number theoretic methods for multiple integration. SIAM J. Numer. Anal. 13, 904-914 (1976).
    • (1976) SIAM J. Numer. Anal. , vol.13 , pp. 904-914
    • Cranley, R.1    Patterson, T.N.L.2
  • 6
    • 0003665885 scopus 로고
    • R. B. D'Agostino and M. A. Stephens (Eds.), New York: Dekker
    • D'Agostino, R. B., Stephens, M. A. (eds.): Goodness-of-Fit Techniques. Dekker, New York (1986).
    • (1986) Goodness-of-Fit Techniques
  • 7
    • 0037678890 scopus 로고    scopus 로고
    • Marcinkiewicz-Zygmund inequalities and the numerical approximation of singular integrals for exponential weights: methods,results and open problems, some new, some old
    • Damelin, S. B.: Marcinkiewicz-Zygmund inequalities and the numerical approximation of singular integrals for exponential weights: methods, results and open problems, some new, some old. J. Complex. 19, 406-415 (2003).
    • (2003) J. Complex. , vol.19 , pp. 406-415
    • Damelin, S.B.1
  • 8
    • 0038392442 scopus 로고    scopus 로고
    • Numerical integration, energy and asymptotic equidistributon on the sphere
    • Damelin, S. B., Grabner, P.: Numerical integration, energy and asymptotic equidistributon on the sphere. J. Complex. 19, 231-246 (2003).
    • (2003) J. Complex. , vol.19 , pp. 231-246
    • Damelin, S.B.1    Grabner, P.2
  • 9
    • 22844454647 scopus 로고    scopus 로고
    • The support of the equilibrium measure for monomial external fields on [-1,1]
    • Damelin, S. B., Kuijlaars, A. B. J.: The support of the equilibrium measure for monomial external fields on [-1, 1]. Trans. Am. Math. Soc. 351, 4561-4584 (1999).
    • (1999) Trans. Am. Math. Soc. , vol.351 , pp. 4561-4584
    • Damelin, S.B.1    Kuijlaars, A.B.J.2
  • 11
    • 0041082478 scopus 로고    scopus 로고
    • The support of the equilibrium measure for a class of external fields on a finite interval
    • Damelin, S. B., Dragnev, P. D., Kuijlaars, A. B. J.: The support of the equilibrium measure for a class of external fields on a finite interval. Pac. J. Math. 199, 303-321 (2001).
    • (2001) Pac. J. Math. , vol.199 , pp. 303-321
    • Damelin, S.B.1    Dragnev, P.D.2    Kuijlaars, A.B.J.3
  • 12
    • 62549106589 scopus 로고    scopus 로고
    • Energies, group-invariant kernels and numerical integration on compact manifolds
    • doi:10.1016/j.jco.2008.09.001
    • Damelin, S. B., Levesley, J., Ragozin, D. L., Sun, X.: Energies, group-invariant kernels and numerical integration on compact manifolds. J. Complex. 25(2), 152-162 (2009). doi: 10. 1016/j. jco. 2008. 09. 001.
    • (2009) J. Complex. , vol.25 , Issue.2 , pp. 152-162
    • Damelin, S.B.1    Levesley, J.2    Ragozin, D.L.3    Sun, X.4
  • 14
    • 0033317391 scopus 로고    scopus 로고
    • Centroidal Voronoi tessellations: applications and algorithms
    • Du, Q., Faber, V., Gunzburger, M.: Centroidal Voronoi tessellations: applications and algorithms. SIAM Rev. 41(4), 637-676 (1999).
    • (1999) SIAM Rev. , vol.41 , Issue.4 , pp. 637-676
    • Du, Q.1    Faber, V.2    Gunzburger, M.3
  • 15
    • 85115723184 scopus 로고    scopus 로고
    • Interdisciplinary Mathematical Sciences, Singapore: World Scientific
    • Fasshauer, G. E.: Meshfree Approximation Methods with Matlab. Interdisciplinary Mathematical Sciences, vol. 6. World Scientific, Singapore (2007).
    • (2007) Meshfree Approximation Methods with Matlab , vol.6
    • Fasshauer, G.E.1
  • 16
    • 84968484404 scopus 로고
    • Spherical designs, discrepancy and numerical integration
    • Grabner, P. J., Tichy, R. F.: Spherical designs, discrepancy and numerical integration. Math. Comput. 60, 327-336 (1993).
    • (1993) Math. Comput. , vol.60 , pp. 327-336
    • Grabner, P.J.1    Tichy, R.F.2
  • 17
    • 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, 1186-1194 (2004).
    • (2004) Not. Am. Math. Soc. , vol.51 , pp. 1186-1194
    • Hardin, D.P.1    Saff, E.B.2
  • 18
    • 0032345316 scopus 로고    scopus 로고
    • A generalized discrepancy and quadrature error bound
    • Hickernell, F. J.: A generalized discrepancy and quadrature error bound. Math. Comput. 67, 299-322 (1998).
    • (1998) Math. Comput. , vol.67 , pp. 299-322
    • Hickernell, F.J.1
  • 19
    • 0001970489 scopus 로고    scopus 로고
    • Goodness-of-fit statistics, discrepancies and robust designs
    • Hickernell, F. J.: Goodness-of-fit statistics, discrepancies and robust designs. Stat. Probab. Lett. 44, 73-78 (1999).
    • (1999) Stat. Probab. Lett. , vol.44 , pp. 73-78
    • Hickernell, F.J.1
  • 20
    • 0002938519 scopus 로고    scopus 로고
    • What affects the accuracy of quasi-Monte Carlo quadrature?
    • H. Niederreiter and J. Spanier (Eds.), Berlin: Springer
    • Hickernell, F. J.: What affects the accuracy of quasi-Monte Carlo quadrature? In: Niederreiter, H., Spanier, J. (eds.) Monte Carlo and Quasi-Monte Carlo Methods 1998, pp. 16-55. Springer, Berlin (2000).
    • (2000) Monte Carlo and Quasi-Monte Carlo Methods 1998 , pp. 16-55
    • Hickernell, F.J.1
  • 23
    • 0001356123 scopus 로고    scopus 로고
    • Digital point sets: analysis and applications
    • Lecture Notes in Statistics, P. Hellekalek and G. Larcher (Eds.), New York: Springer
    • Larcher, G.: Digital point sets: analysis and applications. In: Hellekalek, P., Larcher, G. (eds.) Random and Quasi-Random Point Sets. Lecture Notes in Statistics, vol. 138, pp. 167-222. Springer, New York (1998).
    • (1998) Random and Quasi-Random Point Sets , vol.138 , pp. 167-222
    • Larcher, G.1
  • 24
    • 84990604340 scopus 로고
    • Hecke operators and distributing points on the sphere I
    • Lubotzky, A., Phillips, R., Sarnak, P.: Hecke operators and distributing points on the sphere I. Commun. Pure Appl. Math. 39, 148-186 (1986).
    • (1986) Commun. Pure Appl. Math. , vol.39 , pp. 148-186
    • Lubotzky, A.1    Phillips, R.2    Sarnak, P.3
  • 25
    • 84990576527 scopus 로고
    • Hecke operators and distributing points on the sphere II
    • Lubotzky, A., Phillips, R., Sarnak, P.: Hecke operators and distributing points on the sphere II. Commun. Pure Appl. Math. 40, 401-420 (1987).
    • (1987) Commun. Pure Appl. Math. , vol.40 , pp. 401-420
    • Lubotzky, A.1    Phillips, R.2    Sarnak, P.3
  • 26
    • 84972965080 scopus 로고
    • Weighted polynomials, radial basis functions, and potentials on locally compact spaces
    • Mhaskar, H. N.: Weighted polynomials, radial basis functions, and potentials on locally compact spaces. Numer. Funct. Anal. Optim. 11, 987-1017 (1990/1991).
    • (1990) Numer. Funct. Anal. Optim. , vol.11 , pp. 987-1017
    • Mhaskar, H.N.1
  • 28
    • 3242701678 scopus 로고    scopus 로고
    • On the tractability of multivariate integration and approximation by neural networks
    • Mhaskar, H. N.: On the tractability of multivariate integration and approximation by neural networks. J. Complex. 20, 561-590 (2004).
    • (2004) J. Complex. , vol.20 , pp. 561-590
    • Mhaskar, H.N.1
  • 30
    • 0001142376 scopus 로고    scopus 로고
    • When are integration and discrepancy tractable
    • London Math. Soc. Lecture Note Ser, Cambridge: Cambridge University Press
    • Novak, E., Woźniakowski, H.: When are integration and discrepancy tractable? In: Foundations of Computational Mathematics. London Math. Soc. Lecture Note Ser., vol. 284. Cambridge University Press, Cambridge (2001).
    • (2001) Foundations of Computational Mathematics , vol.284
    • Novak, E.1    Woźniakowski, H.2
  • 31
    • 0008846507 scopus 로고    scopus 로고
    • Monte Carlo, quasi-Monte Carlo, and randomized quasi-Monte Carlo
    • H. Niederreiter and J. Spanier (Eds.), Berlin: Springer
    • Owen, A. B.: Monte Carlo, quasi-Monte Carlo, and randomized quasi-Monte Carlo. In: Niederreiter, H., Spanier, J. (eds.): Monte Carlo and Quasi-Monte Carlo Methods 1998. Springer, Berlin (2000).
    • (2000) Monte Carlo and Quasi-Monte Carlo Methods 1998
    • Owen, A.B.1
  • 34
    • 78449291705 scopus 로고    scopus 로고
    • SAS Institute: JMP 7. 0
    • SAS Institute: JMP 7. 0 (2007).
    • (2007)
  • 35
    • 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, 5977-5987 (1972).
    • (1972) Ark. Mat. , vol.10 , pp. 5977-5987
    • Sjögren, P.1
  • 39
    • 29744465941 scopus 로고    scopus 로고
    • Cambridge Monographs on Applied and Computational Mathematics, Cambridge: Cambridge University Press
    • Wendland, H.: Scattered Data Approximation. Cambridge Monographs on Applied and Computational Mathematics, vol. 17. Cambridge University Press, Cambridge (2005).
    • (2005) Scattered Data Approximation , vol.17
    • Wendland, H.1
  • 40
    • 0037960194 scopus 로고
    • Über die Gleichverteilung der Zahlen mod Eins
    • Weyl, H.: Über die Gleichverteilung der Zahlen mod Eins. Math. Ann. 77, 313-352 (1916).
    • (1916) Math. Ann. , vol.77 , pp. 313-352
    • Weyl, H.1


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