June  2005, 4(2): 389-403. doi: 10.3934/cpaa.2005.4.389

Uniformly distributed points on the sphere

1. 

Department of Mathematics, Southwest Missouri State University, Springfield, MO 65804, United States

Received  March 2004 Revised  December 2004 Published  March 2005

In this work, we present uniformly distributed sequences on the unit sphere, and we show that this property is equivalent to requiring the sequences to have a low discrepancy. Numerical integration over the sphere is taken as a direct application, and the corresponding errors are estimated. Special care is taken in relating these concepts and properties to those for the euclidean case. Several examples of uniformly distributed sequences of nodes (ensembles) are presented.
Citation: Jorge Rebaza. Uniformly distributed points on the sphere. Communications on Pure & Applied Analysis, 2005, 4 (2) : 389-403. doi: 10.3934/cpaa.2005.4.389
[1]

Enrico Gerlach, Charlampos Skokos. Comparing the efficiency of numerical techniques for the integration of variational equations. Conference Publications, 2011, 2011 (Special) : 475-484. doi: 10.3934/proc.2011.2011.475

[2]

Hongguang Xiao, Wen Tan, Dehua Xiang, Lifu Chen, Ning Li. A study of numerical integration based on Legendre polynomial and RLS algorithm. Numerical Algebra, Control & Optimization, 2017, 7 (4) : 457-464. doi: 10.3934/naco.2017028

[3]

Wen Li, Song Wang, Volker Rehbock. A 2nd-order one-point numerical integration scheme for fractional ordinary differential equations. Numerical Algebra, Control & Optimization, 2017, 7 (3) : 273-287. doi: 10.3934/naco.2017018

[4]

David Li-Bland, Pavol Ševera. Integration of exact Courant algebroids. Electronic Research Announcements, 2012, 19: 58-76. doi: 10.3934/era.2012.19.58

[5]

M. M. Rao. Integration with vector valued measures. Discrete & Continuous Dynamical Systems - A, 2013, 33 (11&12) : 5429-5440. doi: 10.3934/dcds.2013.33.5429

[6]

Vinicius Albani, Adriano De Cezaro, Jorge P. Zubelli. On the choice of the Tikhonov regularization parameter and the discretization level: A discrepancy-based strategy. Inverse Problems & Imaging, 2016, 10 (1) : 1-25. doi: 10.3934/ipi.2016.10.1

[7]

E. Camouzis, H. Kollias, I. Leventides. Stable manifold market sequences. Journal of Dynamics & Games, 2018, 5 (2) : 165-185. doi: 10.3934/jdg.2018010

[8]

Frank Fiedler. Small Golay sequences. Advances in Mathematics of Communications, 2013, 7 (4) : 379-407. doi: 10.3934/amc.2013.7.379

[9]

Valentina Casarino, Paolo Ciatti, Silvia Secco. Product structures and fractional integration along curves in the space. Discrete & Continuous Dynamical Systems - S, 2013, 6 (3) : 619-635. doi: 10.3934/dcdss.2013.6.619

[10]

Mauro Fabrizio, Jaime Munõz Rivera. An integration model for two different ethnic groups. Evolution Equations & Control Theory, 2014, 3 (2) : 277-286. doi: 10.3934/eect.2014.3.277

[11]

Robert I McLachlan, Christian Offen, Benjamin K Tapley. Symplectic integration of PDEs using Clebsch variables. Journal of Computational Dynamics, 2019, 6 (1) : 111-130. doi: 10.3934/jcd.2019005

[12]

René Henrion, Christian Küchler, Werner Römisch. Discrepancy distances and scenario reduction in two-stage stochastic mixed-integer programming. Journal of Industrial & Management Optimization, 2008, 4 (2) : 363-384. doi: 10.3934/jimo.2008.4.363

[13]

Vinicius Albani, Adriano De Cezaro. A connection between uniqueness of minimizers in Tikhonov-type regularization and Morozov-like discrepancy principles. Inverse Problems & Imaging, 2019, 13 (1) : 211-229. doi: 10.3934/ipi.2019012

[14]

Nian Li, Xiaohu Tang, Tor Helleseth. A class of quaternary sequences with low correlation. Advances in Mathematics of Communications, 2015, 9 (2) : 199-210. doi: 10.3934/amc.2015.9.199

[15]

Anna Gierzkiewicz, Klaudiusz Wójcik. Lefschetz sequences and detecting periodic points. Discrete & Continuous Dynamical Systems - A, 2012, 32 (1) : 81-100. doi: 10.3934/dcds.2012.32.81

[16]

A. Gasull, Víctor Mañosa, Xavier Xarles. Rational periodic sequences for the Lyness recurrence. Discrete & Continuous Dynamical Systems - A, 2012, 32 (2) : 587-604. doi: 10.3934/dcds.2012.32.587

[17]

Lori Alvin. Toeplitz kneading sequences and adding machines. Discrete & Continuous Dynamical Systems - A, 2013, 33 (8) : 3277-3287. doi: 10.3934/dcds.2013.33.3277

[18]

Martin Swaczyna, Petr Volný. Uniform motions in central fields. Journal of Geometric Mechanics, 2017, 9 (1) : 91-130. doi: 10.3934/jgm.2017004

[19]

Mickaël Kourganoff. Uniform hyperbolicity in nonflat billiards. Discrete & Continuous Dynamical Systems - A, 2018, 38 (3) : 1145-1160. doi: 10.3934/dcds.2018048

[20]

Younghun Hong, Changhun Yang. Uniform Strichartz estimates on the lattice. Discrete & Continuous Dynamical Systems - A, 2019, 39 (6) : 3239-3264. doi: 10.3934/dcds.2019134

2018 Impact Factor: 0.925

Metrics

  • PDF downloads (6)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]