Titlebook: Geometric Discrepancy; An Illustrated Guide Ji?í Matou?ek Book 1999 Springer-Verlag Berlin Heidelberg 1999 Combinatorics.Dimension.Diskrepa

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Book 1999theoretic roots of discrepancy theory, areas related to Ramsey theory and to hypergraphs, and also results supporting eminently practical methods and algorithms for numerical integration and similar tasks. The applications in- clude financial calculations, computer graphics, and computational physic

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0937-5511 Ramsey theory and to hypergraphs, and also results supporting eminently practical methods and algorithms for numerical integration and similar tasks. The applications in- clude financial calculations, computer graphics, and computational physic978-3-642-03941-6978-3-642-03942-3Series ISSN 0937-5511 Series E-ISSN 2197-6783

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Introduction,to the discrepancy of infinite sequences in the unit interval, and we briefly comment on the historical roots of discrepancy in the theory of uniform distribution (Section 1.1). In Section 1.2, we introduce discrepancy in a general geometric setting, as well as some variations of the basic definitio

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Low-Discrepancy Sets for Axis-Parallel Boxes,id, placed in the unit square in an appropriate scale, as in Fig. 2.1(a). It is easy to see that this gives discrepancy of the order .. Another attempt might be n independent random points in the unit square as in Fig. 2.1(b), but these typically have discrepancy about . as well. (In fact, with high

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More Lower Bounds and the Fourier Transform,ther, very powerful method developed by Beck, based on the Fourier transform. Although one can argue that, deep down, this method is actually related to eigenvalues and proofs using orthogonal or near-orthogonal functions, proofs via the Fourier transform certainly look different, being less geometr