QMC Strength for Some Random Configurations on the Sphere

被引：0
|
作者：
de la Torre, Victor [1 ]
Marzo, Jordi [1 ,2 ]
机构：
[1] Univ Barcelona, Dept Matemat & Informat, Gran Via 585, Barcelona 08007, Spain
[2] Ctr Recerca Matemat, Edifici C,Campus Bellaterra, Bellaterra 08193, Spain
来源：
MONTE CARLO AND QUASI-MONTE CARLO METHODS, MCQMC 2022 | 2024年 / 460卷
关键词：
Random point processes; QMC design; Sphere; Discrepancy; Discrete energy; INTEGRATION; POINTS;
D O I：
10.1007/978-3-031-59762-6_31
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A sequence (X-N) subset of S-d of N-point sets from the d-dimensional sphere has QMC strength s * > d/2 if it has worst-case error of optimal order, N-s/d, for Sobolev spaces of order s for all d/2 < s < s*, and the order is not optimal for sgreaterthanSuperscriptasteriskBaselineperiod s > s*. In [15] conjectured values of the strength are given for some well known point families S-2 based on numerical results. We study the average QMC strength for some related random configurations.
引用
收藏
页码：625 / 642
页数：18
相关论文
共 50 条
  • [31] Casimir forces in multi-sphere configurations
    Babington, James
    Scheel, Stefan
    JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2010, 43 (21)
  • [32] Section problems for configurations of points on the Riemann sphere
    Chen, Lei
    Salter, Nick
    ALGEBRAIC AND GEOMETRIC TOPOLOGY, 2020, 20 (06): : 3047 - 3082
  • [33] Gaussian random fields on the sphere and sphere cross line
    Bingham, Nicholas H.
    Symons, Tasmin L.
    STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2022, 150 : 788 - 801
  • [34] Relative equilibrium configurations of point vortices on a sphere
    Demina, Maria V.
    Kudryashov, Nikolai A.
    REGULAR & CHAOTIC DYNAMICS, 2013, 18 (04): : 344 - 355
  • [35] A CROSSOVER FOR THE BAD CONFIGURATIONS OF RANDOM WALK IN RANDOM SCENERY
    Blachere, Sebastien
    den Hollander, Frank
    Steif, Jeffrey E.
    ANNALS OF PROBABILITY, 2011, 39 (05): : 2018 - 2041
  • [36] Intrinsic random functions on the sphere
    Huang, Chunfeng
    Zhang, Haimeng
    Robeson, Scott M.
    Shields, Jacob
    STATISTICS & PROBABILITY LETTERS, 2019, 146 : 7 - 14
  • [37] MODELING OF A RANDOM FIELD ON A SPHERE
    SIZOVA, AF
    TOVSTIK, TM
    VESTNIK LENINGRADSKOGO UNIVERSITETA SERIYA MATEMATIKA MEKHANIKA ASTRONOMIYA, 1984, (01): : 118 - 120
  • [38] SOME COMBINATORIAL CONFIGURATIONS
    HANANI, H
    TRANSACTIONS OF THE NEW YORK ACADEMY OF SCIENCES, 1968, 30 (03): : 421 - &
  • [39] SOME TACTICAL CONFIGURATIONS
    HANANI, H
    CANADIAN JOURNAL OF MATHEMATICS, 1963, 15 (04): : 702 - &
  • [40] RANDOM LATTICES AND RANDOM SPHERE PACKINGS: TYPICAL PROPERTIES
    Shlosman, Senya
    Tsfasman, Michael A.
    MOSCOW MATHEMATICAL JOURNAL, 2001, 1 (01) : 73 - 89
12345