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| 1 | +Recursive Zonal Equal Area (EQ) Sphere Partitioning Toolbox. |
| 2 | +Release 1.10 2005-06-26 |
| 3 | +Copyright 2004-2005 Paul Leopardi for the University of New South Wales. |
| 4 | +AUTHORS |
| 5 | + |
| 6 | +For licensing, see COPYING. |
| 7 | +For revision history, see CHANGELOG. |
| 8 | + |
| 9 | +Origin |
| 10 | +------ |
| 11 | + Maple and Matlab code is based on Ed Saff [SafSP], [Saf03] |
| 12 | + and Ian Sloan [Slo03]. |
| 13 | + |
| 14 | +References |
| 15 | +---------- |
| 16 | + [Dahl78] B. E. J. Dahlberg, |
| 17 | + "On the distribution of Fekete points", |
| 18 | + Duke Math. J. 45 (1978), no. 3, pp. 537--542. |
| 19 | + |
| 20 | + [KuiS98]: A. B. J. Kuijlaars, E. B. Saff, |
| 21 | + "Asymptotics for minimal discrete energy on the sphere", |
| 22 | + Transactions of the American Mathematical Society, v. 350 no. 2 (Feb 1998) |
| 23 | + pp. 523--538. |
| 24 | + |
| 25 | + [KuiSS04]: A. B. J. Kuijlaars, E. B. Saff, X. Sun, |
| 26 | + "Minimum separation f the minimal energy points on spheres in Euclidean |
| 27 | + spaces", (preprint) 2004-11-30. |
| 28 | + |
| 29 | + [LeGS01]: T. Le Gia, I. H. Sloan, |
| 30 | + "The uniform norm of hyperinterpolation on the unit sphere in an arbitrary |
| 31 | + number of dimensions", Constructive Approximation (2001) 17: p249-265. |
| 32 | + |
| 33 | + [Leo05]: P. Leopardi, |
| 34 | + "A partition of the unit sphere into regions of equal area and small diameter", |
| 35 | + Applied Maths Report AMR05/18, May, 2005, submitted to |
| 36 | + Electronic Transactions on Numerical Analysis. |
| 37 | + http://www.maths.unsw.edu.au/applied/files/2005/amr05_18.pdf |
| 38 | + |
| 39 | + [Mue98]: C. Mueller, "Analysis of spherical symmetries in Euclidean spaces", |
| 40 | + Springer, 1998. |
| 41 | + |
| 42 | + [RakSZ94]: E. A. Rakhmanov, E. B. Saff, Y. M. Zhou, |
| 43 | + "Minimal discrete energy on the sphere", |
| 44 | + Mathematics Research Letters, 1 (1994), pp. 647--662. |
| 45 | + |
| 46 | + [RakSZ95]: E. A. Rakhmanov, E. B. Saff, Y. M. Zhou, |
| 47 | + "Electrons on the sphere", |
| 48 | + Computational methods and function theory 1994 (Penang), pp. 293--309, |
| 49 | + Ser. Approx. Decompos., 5, World Sci. Publishing, River Edge, NJ, 1995. |
| 50 | + |
| 51 | + [SafK97]: E. B. Saff, A. B. J. Kuijlaars, |
| 52 | + "Distributing many points on a sphere", |
| 53 | + Mathematical Intelligencer, v19 no1 (1997), pp. 5--11. |
| 54 | + |
| 55 | + [SafSP]: E. B. Saff, "Sphere Points," |
| 56 | + http://www.math.vanderbilt.edu/~esaff/sphere_points.html |
| 57 | + |
| 58 | + [Saf03]: Ed Saff, "Equal-area partitions of sphere", |
| 59 | + Presentation at UNSW, 2003-07-28. |
| 60 | + |
| 61 | + [Slo03]: Ian Sloan, "Equal area partition of S^3", Notes, 2003-07-29. |
| 62 | + |
| 63 | + [WeiMW]: E. W. Weisstein, |
| 64 | + "Hypersphere." From MathWorld--A Wolfram Web Resource. |
| 65 | + http://mathworld.wolfram.com/Hypersphere.html |
| 66 | + |
| 67 | + [Zho95]: Y. M. Zhou, "Arrangement of points on the sphere", |
| 68 | + Thesis, University of South Florida, 1995. |
| 69 | + |
| 70 | + [Zho98]: Y. M. Zhou, "Equidistribution and extremal energy of N points on |
| 71 | + the sphere", Modelling and computation for applications in mathematics, |
| 72 | + science, and engineering (Evanston, IL, 1996), pp. 39--57, |
| 73 | + Numer. Math. Sci. Comput., Oxford Univ. Press, New York, 1998. |
| 74 | + |
| 75 | +Installation and Utilities |
| 76 | +-------------------------- |
| 77 | +Toolbox Installer 2.2, 2003-07-22 by B. Rasmus Anthin. |
| 78 | +Matlab Central File Exchange |
| 79 | +http://www.mathworks.com/matlabcentral/fileexchange/ |
| 80 | +Home page of B. Rasmus Anthin |
| 81 | +http://www.etek.chalmers.se/~e8rasmus/ |
| 82 | + |
| 83 | +Files modified and relicenced with permission of B. Rasmus Anthin: |
| 84 | +./private |
| 85 | +install.m uninstall.m |
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