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This is a survey (21 pages, 124 references) written for the MCQMC 2014 conference in Leuven, April 2014.
On irregularities of distributions
K. F. Roth · 1954
Earlier work this paper cites.
Quadrature and interpolation formulas for tensor products of certain classes of functions
S. A. Smolyak · 1963
Earlier work this paper cites.
On the optimality of linear methods for operator approximation in convex classes of functions
N. S. Bakhvalov · 1971
Earlier work this paper cites.
Asymptotically sharp bounds for the remainder for the best quadrature formulas for several classes of functions
V. F. Babenko · 1976
Earlier work this paper cites.
Exact asymptotics of the error of weighted cubature formulas optimal for certain classes of functions
V. F. Babenko · 1976
Earlier work this paper cites.
Upper bounds on the error of quadrature formulas on classes of functions
K. K. Frolov · 1976
Earlier work this paper cites.
Upper bounds on the discrepancy in L p L_{p} , 2 ≤ p < ∞ 2\leq p<\infty ,
K. K. Frolov · 1977
Earlier work this paper cites.
Optimal numerical integration formulas for some classes of functions
A. G. Sukharev · 1979
Earlier work this paper cites.
On irregularities of distributions IV
K. F. Roth · 1980
Earlier work this paper cites.
A General Theory of Optimal Algorithms
J. F. Traub and H. Woźniakowski · 1980
Earlier work this paper cites.
On the correct order of the error of optimal cubature formulas in spaces with dominant derivative, and on quadratic deviations of grids
V. A. Bykovskii · 1985
Earlier work this paper cites.
A geometric inequality and the complexity of computing volume
G. Elekes · 1986
Earlier work this paper cites.
Approximate recovery of periodic functions of several variables
V. N. Temlyakov · 1987
Earlier work this paper cites.
Deterministic and Stochastic Error Bounds in Numerical Analysis
E. Novak · 1988
Earlier work this paper cites.
Information-Based Complexity
J. F. Traub, G. W. Wasilkowski, and H. Woźniakowski · 1988
Earlier work this paper cites.
Random volumes in the n n -cube
M. E. Dyer, Z. Füredi, and C. McDiarmid · 1990
Earlier work this paper cites.
Optimal cubature formulas in the classes D 2 1 , c D_{2}^{1,c} and D 2 1 , l 1 D_{2}^{1,l_{1}}
Maung Zho Newn and I. F. Sharygin · 1991
Earlier work this paper cites.
Lower bounds for the complexity of Monte Carlo function approximation
S. Heinrich · 1992
Earlier work this paper cites.
Random Number Generation and Quasi-Monte Carlo Methods
H. Niederreiter · 1992
Earlier work this paper cites.
On a way of obtaining lower estimates for the error of quadrature formulas
V. N. Temlyakov · 1992
Earlier work this paper cites.
On approximate recovery of functions with bounded mixed derivative
V. N. Temlyakov · 1993
Earlier work this paper cites.
Random approximation in numerical analysis
S. Heinrich · 1994
Earlier work this paper cites.
Asymptotically exact estimation of the error of weighted cubature formulas optimal in some classes of continuous functions
E. V. Chernaya · 1995
Earlier work this paper cites.
The optimal error of Monte Carlo integration
P. Mathé · 1995
Earlier work this paper cites.
Constructions of uniform distributions in terms of geometry of numbers
M. M. Skriganov · 1995
Earlier work this paper cites.
Explicit cost bounds of algorithms for multivariate tensor product problems
G. W. Wasilkowski and H. Woźniakowski · 1995
Earlier work this paper cites.
Complexity of Monte Carlo algorithms
S. Heinrich · 1996
Earlier work this paper cites.
On the power of adaption
E. Novak · 1996
Earlier work this paper cites.
High dimensional integration of smooth functions over cubes
E. Novak and K. Ritter · 1996
Earlier work this paper cites.
On tractability of path integration
G. W. Wasilkowski and H. Woźniakowski · 1996
Earlier work this paper cites.
Cubature formulas for Besov classes
V. V. Dubinin · 1997
Earlier work this paper cites.
The curse of dimension and a universal method for numerical integration
E. Novak and K. Ritter · 1997
Earlier work this paper cites.
Tractability of tensor product linear operators
E. Novak, I. H. Sloan, and H. Woźniakowski · 1997
Earlier work this paper cites.
When are quasi-Monte Carlo algorithms efficient for high dimensional integrals?
I. H. Sloan and H. Woźniakowski · 1998
Earlier work this paper cites.
Simple cubature formulas with high polynomial exactness
E. Novak and K. Ritter · 1999
Earlier work this paper cites.
Weighted tensor-product algorithms for linear multivariate problems
G. W. Wasilkowski and H. Woźniakowski · 1999
Earlier work this paper cites.
Integration and approximation in arbitrary dimension
F. J. Hickernell and H. Woźniakowski · 2000
Earlier work this paper cites.
Quantum Summation with an Application to Integration
S. Heinrich · 2001
Earlier work this paper cites.
The inverse of the star-discrepancy depends linearly on the dimension
S. Heinrich, E. Novak, G. W. Wasilkowski, and H. Woźniakowski · 2001
Earlier work this paper cites.
Tractability of multivariate integration for periodic functions
F. J. Hickernell and H. Woźniakowski · 2001
Earlier work this paper cites.
Quantum complexity of integration
E. Novak · 2001
Cited alongside, same era.
Intractability results for integration and discrepancy
E. Novak and H. Woźniakowski · 2001
Cited alongside, same era.
Explicit constructions in the classical mean squares problem in irregularities of point distribution
W. W. L. Chen and M. M. Skriganov · 2002
Cited alongside, same era.
Optimal summation and integration by deterministic, randomized, and quantum algorithms. In K.-T. Fang, F. J. Hickernell, and H. Niederreiter, editors, Monte Carlo and Quasi-Monte Carlo Methods 2000
S. Heinrich and E. Novak · 2002
Cited alongside, same era.
On the step-by-step construction of quasi-Monte Carlo integration rules that achieves strong tractability error bounds in weighted Sobolev spaces
I. H. Sloan, F. Y. Kuo, and S. Joe · 2002
Cited alongside, same era.
Exponential convergence and tractability of multivariate integration for Korobov spaces
J. Dick, G. Larcher, F. Pillichshammer, and H. Woźniakowski · 2011
Later among the works it cites.
Deterministic multi-level algorithms for infinite-dimensional integration on ℝ ℕ \mathbb{R}^{\mathbb{N}}
B. Niu, F. Hickernell, Th. Müller-Gronbach, and K. Ritter · 2011
Later among the works it cites.
Lower bounds on the complexity for linear functionals in the randomized setting
E. Novak and H. Woźniakowski · 2011
Later among the works it cites.
Tractability of infinite-dimensional integration in the worst case and randomized settings
L. Plaskota and G. W. Wasilkowski · 2011
Later among the works it cites.
Spline interpolation on sparse grids
W. Sickel and T. Ullrich · 2011
Later among the works it cites.
Efficient calculation of the worst-case error and (fast) component-by-component construction of higher order polynomial lattice rules
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Component-by-component construction of good lattice rules
I. H. Sloan and A. V. Reztsov · 2002
Cited alongside, same era.
Quantum integration in Sobolev spaces
S. Heinrich · 2003
Cited alongside, same era.
Component-by-component constructions achieve the optimal rate of convergence for multivariate integration in weighted Korobov and Sobolev spaces
F. Y. Kuo · 2003
Cited alongside, same era.
Cubature formulas, discrepancy, and nonlinear approximation
V. N. Temlyakov · 2003
Cited alongside, same era.
Path integration on a quantum computer
J. F. Traub and H. Woźniakowski · 2003
Cited alongside, same era.
Sparse grids
H.-J. Bungartz and M. Griebel · 2004
Cited alongside, same era.
Linear vs. nonlinear algorithms for linear problems
J. Creutzig and P. Wojtaszczyk · 2004
Cited alongside, same era.
J. Baldeaux, J. Dick, G. Leobacher, D. Nuyens, and F. Pillichshammer · 2012
Later among the works it cites.
Infinite-dimensional integration on weighted Hilbert spaces
M. Gnewuch · 2012
Later among the works it cites.
Entropy, randomization, derandomization, and discrepancy
M. Gnewuch · 2012
Later among the works it cites.
Monte-Carlo-Algorithmen
Th. Müller-Gronbach, E. Novak, and K. Ritter · 2012
Later among the works it cites.
Tractability of Multivariate Problems , Volume III: Standard Information for Operators
E. Novak and H. Woźniakowski · 2012
Later among the works it cites.
Explicit error bounds for Markov chain Monte Carlo
D. Rudolf · 2012
Later among the works it cites.
Complexity of Banach space valued and parametric integration
T. Daun and S. Heinrich · 2013
Later among the works it cites.
High-dimensional integration: The quasi-Monte Carlo way
J. Dick, F. Y. Kuo, and I. H. Sloan · 2013
Later among the works it cites.
Lower error bounds for randomized multilevel and changing dimension algorithms
M. Gnewuch · 2013
Later among the works it cites.
Discrepancy, integration and tractability
A. Hinrichs · 2013
Later among the works it cites.
Probabilistic discrepancy bounds for Monte Carlo point sets
Ch. Aistleitner and M. Hofer · 2014
Closest in time.
Optimal randomized multilevel algorithms for infinite-dimensional integration on function spaces with ANOVA-type decomposition
J. Baldeaux and M. Gnewuch · 2014
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The cost of deterministic, adaptive, automatic algorithms: Cones, not balls
N. Clancy, Y. Ding, C. Hamilton, F. J. Hickernell, and Y. Zhang · 2014
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Complexity of parametric integration in various smoothness classes
T. Daun and S. Heinrich · 2014
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Numerical integration of Hölder continuous, absolutely convergent Fourier-, Fourier cosine-, and Walsh series
J. Dick · 2014
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Optimal randomized changing dimension algorithms for infinite-dimensional integration on function spaces with ANOVA-type decomposition
J. Dick and M. Gnewuch · 2014
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Infinite-dimensional integration in weighted Hilbert spaces: anchored decompositions, optimal deterministic algorithms, and higher order convergence
J. Dick and M. Gnewuch · 2014
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Discrepancy theory and quasi-Monte Carlo integration
J. Dick and F. Pillichshammer · 2014
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A lower bound for the discrepancy of a random point set
B. Doerr · 2014
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Calculation of discrepancy measures and applications
C. Doerr, M. Gnewuch, and M. Wahlström · 2014
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On weighted Hilbert spaces and integration of functions of infinitely many variables
M. Gnewuch, S. Mayer, and K. Ritter · 2014
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The curse of dimensionality for numerical integration of smooth functions
A. Hinrichs, E. Novak, M. Ullrich, and H. Woźniakowski · 2014
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The curse of dimensionality for numerical integration of smooth functions II
A. Hinrichs, E. Novak, M. Ullrich, and H. Woźniakowski · 2014
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On weak tractability of the Clenshaw Curtis Smolyak algorithm
A. Hinrichs, E. Novak, and M. Ullrich · 2014
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Multivariate integration of infinitely many times differentiable functions in weighted Korobov spaces
P. Kritzer, F. Pillichshammer, and H. Woźniakowski · 2014
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Tractability of multivariate analytic problems
P. Kritzer, F. Pillichshammer, and H. Woźniakowski · 2014
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Introduction to Quasi-Monte Carlo Integration and Applications
G. Leobacher and F. Pillichshammer · 2014
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Computation of expectations by Markov chain Monte Carlo methods
E. Novak and D. Rudolf · 2014
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On “Upper error bounds for quadrature formulas on function classes” by K. K. Frolov
M. Ullrich · 2014
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Weak and quasi-polynomial tractability of approximation of infinitely differentiable functions
J. Vybíral · 2014
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Average case tractability of approximating ∞ \infty -variate functions
G. W. Wasilkowski · 2014
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On the approximate calculation of multiple integrals
N. S. Bakhvalov · 2015
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Lower bounds for the integration error for multivariate functions with mixed smoothness and optimal Fibonacci cubature for functions on the square
Dinh Dũng and T. Ullrich · 2015
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Complexity of oscillatory integration for univariate Sobolev spaces
E. Novak, M. Ullrich, and H. Woźniakowski · 2015
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