Construction Algorithms for Digital Nets with Low Weighted Star Discrepancy

2005 ◽  
Vol 43 (1) ◽  
pp. 76-95 ◽  
Author(s):  
Josef Dick ◽  
Gunther Leobacher ◽  
Friedrich Pillichshammer
Keyword(s):  
Star Discrepancy ◽  
Construction Algorithms ◽  
Digital Nets

scholarly journals Constructions of general polynomial lattices for multivariate integration

2007 ◽  
Vol 76 (1) ◽  
pp. 93-110 ◽  
Author(s):  
Peter Kritzer ◽  
Friedrich Pillichshammer
Keyword(s):  
Hilbert Spaces ◽  
Lattice Rules ◽  
Irreducible Polynomials ◽  
Worst Case ◽  
Multivariate Integration ◽  
Construction Algorithm ◽  
General Polynomial ◽  
Construction Algorithms ◽  
Digital Nets

We study a construction algorithm for certain polynomial lattice rules modulo arbitrary polynomials. The underlying polynomial lattices are special types of digital nets as introduced by Niederreiter. Dick, Kuo, Pillichshammer and Sloan recently introduced construction algorithms for polynomial lattice rules modulo irreducible polynomials which yield a small worst-case error for integration of functions in certain weighted Hilbert spaces. Here, we generalize these results to the case where the polynomial lattice rules are constructed moduloarbitrarypolynomials.

scholarly journals Improved upper bounds for the star discrepancy of digital nets in dimension 3

2003 ◽  
Vol 108 (2) ◽  
pp. 167-189 ◽  
Author(s):  
Friedrich Pillichshammer
Keyword(s):  
Upper Bounds ◽  
Star Discrepancy ◽  
Digital Nets

Weighted Star Discrepancy of Digital Nets in Prime Bases

2006 ◽  
pp. 77-96 ◽  
Author(s):  
Josef Dick ◽  
Harald Niederreiter ◽  
Friedrich Pillichshammer
Keyword(s):  
Star Discrepancy ◽  
Digital Nets

Digital Nets and Sequences

2009 ◽  
Author(s):  
Josef Dick ◽  
Friedrich Pillichshammer
Keyword(s):  
Digital Nets

Dimension-Descending Algorithm for Spherical Delaunay Triangulation

2011 ◽  
Vol 130-134 ◽  
pp. 2915-2919
Author(s):  
Ping Duan ◽  
Jia Tian Li ◽  
Jia Li
Keyword(s):  
Delaunay Triangulation ◽  
Time Complexity ◽  
Image Point ◽  
Spherical Space ◽  
Projected Image ◽  
Plane Image ◽  
Projection Center ◽  
Space Data ◽  
Construction Algorithms ◽  
Main Construction

Spherical Delaunay triangulation (SDT) which is a powerful tool to represent, organize and analyze spherical space data has become a focus of spherical GIS research. Projection stitching algorithm is one of the main construction algorithms of SDT. The basic idea of stitching algorithm is that the sphere is divided into two hemispheres to avoid projected image point coincidence. So, the practicality of projection stitching algorithm is lower because of merging two hemispheres. Aimed at the disadvantage of projection stitching algorithm, this paper puts forward a new algorithm to construct SDT used perspective projection principle. The projection center is placed on sphere to establish one-to-one mapping between spherical space points and plane image points. Experiment shows that the time complexity of our algorithm depends on Delaunay triangulation construction algorithm of the plane.

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