%0 Generic

%T Uniform Distribution and Quasi-Monte Carlo Methods Discrepancy, Integration and Applications

%A Kritzer, Peter

%A Niederreiter, Harald

%A Pillichshammer, Friedrich

%A Winterhof, Arne

%I De Gruyter

%@ 9783110317947

%@ 9783110317930

%K Monte Carlo method

%K Uniform distribution (Probability theory)

%K Monte Carlo method.

%K Uniform distribution (Probability theory).

%K Gleichmäßige Verteilung.

%K Mathematik.

%K Monte-Carlo-Simulation.

%K Gleichmäßige Verteilung Quasi-Monte-Carlo-Methode

%K MATHEMATICS / Number Theory

%K Electronic books

%K Konferenzschrift

%K Konferenzschrift 2013 Linz

%K Gleichmäßige Verteilung

%K Monte-Carlo-Simulation

%D 2014

%X Literaturangaben

%X Preface; Contents; Metric number theory, lacunary series and systems of dilated functions; 1 Uniform distribution modulo 1; 2 Metric number theory; 3 Discrepancy; 4 Lacunary series; 5 Almost everywhere convergence; 6 Sums involving greatest common divisors; Strong uniformity; 1 Introduction; 2 Superuniformity and super-duper uniformity; 2.1 Superuniformity of the typical billiard paths; 2.2 Super-duper uniformity of the 2-dimensional ray; 3 Superuniformmotions; 3.1 Billiards in other shapes; 3.2 Superuniformity of the geodesics on an equifacial tetrahedron surface

%X Discrepancy theory and harmonic analysis1 Introduction; 2 Exponential sums; 3 Fourier analysis methods; 3.1 Rotated rectangles; 3.2 The lower bound for circles; 3.3 Further remarks; 4 Dyadic harmonic analysis: discrepancy function estimates; 4.1 Lp -discrepancy, 1 < p < ∞ ; 4.2 The L∞discrepancy estimates; 4.3 The other endpoint, L1; Explicit constructions of point sets and sequences with low discrepancy; 1 Introduction; 2 Lower bounds; 3 Upper bounds; 4 Digital nets and sequences; 5 Walsh series expansion of the discrepancy function

%X 6 The construction of finite point sets according to Chen and Skriganov7 The construction of infinite sequences according to Dick and Pillichshammer; 8 Extensions to the Lqdiscrepancy; 9 Extensions to Orlicz norms of the discrepancy function; Subsequences of automatic sequences and uniform distribution; 1 Introduction; 2 Automatic sequences; 3 Subsequences along the sequence nc; 4 Polynomial subsequences; 5 Subsequences along the primes; On Atanassov's methods for discrepancy bounds of low-discrepancy sequences; 1 Introduction; 2 Atanassov's methods for Halton sequences

%X 2.1 Review of Halton sequences2.2 Review of previous bounds for the discrepancy of Halton sequences; 2.3 Atanassov's methods applied to Halton sequences; 2.4 Scrambling Halton sequences with matrices; 3 Atanassov's method for(t,s)-sequences ; 3.1 Review of (t,s)-sequences; 3.2 Review of bounds for the discrepancy of (t,s)-sequences; 3.3 Atanassov'smethod applied to (t,s)-sequences; 3.4 The special case of even bases for (t,s)-sequences; 4 Atanassov's methods for generalized Niederreiter sequences and (??, e, ??)- sequences; The hybrid spectral test: a unifying concept; 1 Introduction

%X 2 Adding digit vectors3 Notation; 4 The hybrid spectral test; 5 Examples; 5.1 Example I: Integration lattices; 5.2 Example II: Extreme and star discrepancy; Tractability of multivariate analytic problems; 1 Introduction; 2 Tractability; 3 A weighted Korobov space of analytic functions; 4 Integration in H(Ks,a,b) ; 5 L2-approximation inH(Ks,a,b); 6 Conclusion and outlook; Discrepancy estimates for sequences: new results and open problems; 1 Introduction; 2 Metrical and average type discrepancy estimates for digital point sets and sequences and for good lattice point sets

%X 3 Discrepancy estimates for and applications of hybrid sequences

%C De Gruyter

%C Berlin [u.a.]

%U http://slubdd.de/katalog?TN_libero_mab2