When are quasi-Monte Carlo algorithms efficient for high dimensional integrals?

SIGACT news complexity theory column 31

ACM SIGACT News

The Brownian bridge does not offer a consistent advantage in Quasi-Monte Carlo integration

Journal of Complexity

Tractability of integration in non-periodic and periodic weighted tensor product Hilbert spaces

Journal of Complexity

A constructive approach to strong tractability using Quasi-Monte Carlo algorithms

Journal of Complexity

Discrepancy Theory and Its Application to Finance

TCS '00 Proceedings of the International Conference IFIP on Theoretical Computer Science, Exploring New Frontiers of Theoretical Informatics

Strong tractability of multivariate integration using quasi-Monte Carlo algorithms

Mathematics of Computation

On the step-by-step construction of quasi: Monte Carlo integration rules that achieve strong tractability error bounds in weighted Sobolev spaces

Mathematics of Computation

The error bounds and tractability of quasi-Monte Carlo algorithms in infinite dimension

Mathematics of Computation

The effective dimension and quasi-Monte Carlo integration

Journal of Complexity

Component-by-component constructions achieve the optimal rate of convergence for multivariate integration in weighted Korobov and Sobolev spaces

Journal of Complexity

Sufficient conditions for fast quasi-Monte Carlo convergence

Journal of Complexity

My dream quadrature rule

Journal of Complexity

Open problems for tractability of multivariate integration

Journal of Complexity

On the tractability of the Brownian bridge algorithm

Journal of Complexity

Bounds for the weighted Lp discrepancy and tractability of integration

Journal of Complexity

Integration error for multivariate functions from anisotropic classes

Journal of Complexity

I-binomial scrambling of digital nets and sequences

Journal of Complexity

Finite-order weights imply tractability of multivariate integration

Journal of Complexity

On the convergence rate of the component-by-component construction of good lattice rules

Journal of Complexity

Liberating the weights

Journal of Complexity

On polynomial-time property for a class of randomized quadratures

Journal of Complexity

On the root mean square weighted L2 discrepancy of scrambled nets

Journal of Complexity

Finite-order weights imply tractability of linear multivariate problems

Journal of Approximation Theory

Multivariate integration in weighted Hilbert spaces based on Walsh functions and weighted Sobolev spaces

Journal of Complexity

Quasi-Monte Carlo methods can be efficient for integration over products of spheres

Journal of Complexity

Information-based complexity

Encyclopedia of Computer Science

Diaphony, discrepancy, spectral test and worst-case error

Mathematics and Computers in Simulation

On the necessity of low-effective dimension

Journal of Complexity

Fast component-by-component construction of rank-1 lattice rules with a non-prime number of points

Journal of Complexity - Special issue: Algorithms and complexity for continuous problems Schloss Dagstuhl, Germany, September 2004

Randomly shifted lattice rules on the unit cube for unbounded integrands in high dimensions

Journal of Complexity - Special issue: Algorithms and complexity for continuous problems Schloss Dagstuhl, Germany, September 2004

The weighted b-adic diaphony

Journal of Complexity

On the mean square weighted L2 discrepancy of randomized digital nets in prime base

Journal of Complexity - Special issue: Information-based complexity workshops FoCM conference Santander, Spain, July 2005

Randomly shifted lattice rules for unbounded integrands

Journal of Complexity - Special issue: Information-based complexity workshops FoCM conference Santander, Spain, July 2005

Exact cubature for a class of functions of maximum effective dimension

Journal of Complexity - Special issue: Information-based complexity workshops FoCM conference Santander, Spain, July 2005

A component-by-component approach to efficient numerical integration over products of spheres

Journal of Complexity

Tractability of quasilinear problems I: General results

Journal of Approximation Theory

On the Effects of Dimension Reduction Techniques on Some High-Dimensional Problems in Finance

Operations Research

Generalized tractability for multivariate problems Part I

Journal of Complexity

DCMA: yet another derandomization in covariance-matrix-adaptation

Proceedings of the 9th annual conference on Genetic and evolutionary computation

On the existence of higher order polynomial lattices based on a generalized figure of merit

Journal of Complexity

Strong tractability of multivariate integration of arbitrary high order using digitally shifted polynomial lattice rules

Journal of Complexity

Low discrepancy sequences in high dimensions: How well are their projections distributed?

Journal of Computational and Applied Mathematics

New Brownian bridge construction in quasi-Monte Carlo methods for computational finance

Journal of Complexity

Tractability properties of the weighted star discrepancy

Journal of Complexity

When Does Quasi-random Work?

Proceedings of the 10th international conference on Parallel Problem Solving from Nature: PPSN X

On efficient Monte Carlo-based statistical static timing analysis of digital circuits

Proceedings of the 2008 IEEE/ACM International Conference on Computer-Aided Design

Efficient Conjoint Choice Designs in the Presence of Respondent Heterogeneity

Marketing Science

New averaging technique for approximating weighted integrals

Journal of Complexity

Why one must use reweighting in estimation of distribution algorithms

Proceedings of the 11th Annual conference on Genetic and evolutionary computation

Optimizing low-discrepancy sequences with an evolutionary algorithm

Proceedings of the 11th Annual conference on Genetic and evolutionary computation

Dimension Reduction Techniques in Quasi-Monte Carlo Methods for Option Pricing

INFORMS Journal on Computing

Learning a function from noisy samples at a finite sparse set of points

Journal of Approximation Theory

On the approximation of smooth functions using generalized digital nets

Journal of Complexity

Tractability of the Helmholtz equation with non-homogeneous Neumann boundary conditions: The relation to the L2-approximation

Journal of Complexity

Multi-element probabilistic collocation method in high dimensions

Journal of Computational Physics

A practical view of randomized quasi-Monte Carlo: invited presentation, extended abstract

Proceedings of the Fourth International ICST Conference on Performance Evaluation Methodologies and Tools

Finite-order weights imply tractability of linear multivariate problems

Journal of Approximation Theory

On the necessity of low-effective dimension

Journal of Complexity

Fast component-by-component construction of rank-1 lattice rules with a non-prime number of points

Journal of Complexity - Special issue: Algorithms and complexity for continuous problems Schloss Dagstuhl, Germany, September 2004

Randomly shifted lattice rules on the unit cube for unbounded integrands in high dimensions

Journal of Complexity - Special issue: Algorithms and complexity for continuous problems Schloss Dagstuhl, Germany, September 2004

Randomly shifted lattice rules with the optimal rate of convergence for unbounded integrands

Journal of Complexity

Liberating the dimension

Journal of Complexity

Dimension-wise integration of high-dimensional functions with applications to finance

Journal of Complexity

Advanced variance reduction and sampling techniques for efficient statistical timing analysis

IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems

Approximation of Bayesian Inverse Problems for PDEs

SIAM Journal on Numerical Analysis

Quasi-Monte Carlo Methods in Financial Engineering: An Equivalence Principle and Dimension Reduction

Operations Research

Quasi-Monte Carlo methods for elliptic PDEs with random coefficients and applications

Journal of Computational Physics

Construction algorithms for higher order polynomial lattice rules

Journal of Complexity

Existence and construction of shifted lattice rules with an arbitrary number of points and bounded weighted star discrepancy for general decreasing weights

Journal of Complexity

Weighted geometric discrepancies and numerical integration on reproducing kernel Hilbert spaces

Journal of Complexity

Tractability results for weighted Banach spaces of smooth functions

Journal of Complexity

Tensor-Train Decomposition

SIAM Journal on Scientific Computing

Adaptive ANOVA decomposition of stochastic incompressible and compressible flows

Journal of Computational Physics

Evolutionary optimization of low-discrepancy sequences

ACM Transactions on Modeling and Computer Simulation (TOMACS)

Efficient calculation of the worst-case error and (fast) component-by-component construction of higher order polynomial lattice rules

Numerical Algorithms

How do path generation methods affect the accuracy of quasi-Monte Carlo methods for problems in finance?

Journal of Complexity

Variance bounds and existence results for randomly shifted lattice rules

Journal of Computational and Applied Mathematics

Randomized Halton sequences

Mathematical and Computer Modelling: An International Journal

Constructions of general polynomial lattice rules based on the weighted star discrepancy

Finite Fields and Their Applications

A New Randomized Algorithm to Approximate the Star Discrepancy Based on Threshold Accepting

SIAM Journal on Numerical Analysis

Error Estimates for the ANOVA Method with Polynomial Chaos Interpolation: Tensor Product Functions

SIAM Journal on Scientific Computing

Enhancing Quasi-Monte Carlo Methods by Exploiting Additive Approximation for Problems in Finance

SIAM Journal on Scientific Computing

Constructing adapted lattice rules using problem-dependent criteria

Proceedings of the Winter Simulation Conference

Numerical solution of the Stratonovich- and Ito-Euler equations: Application to the stochastic piston problem

Journal of Computational Physics

Numerical properties of generalized discrepancies on spheres of arbitrary dimension

Journal of Complexity

Pricing and Hedging with Discontinuous Functions: Quasi--Monte Carlo Methods and Dimension Reduction

Management Science

Better estimation of small sobol' sensitivity indices

ACM Transactions on Modeling and Computer Simulation (TOMACS)

Highly efficient numerical algorithm based on random trees for accelerating parallel Vlasov-Poisson simulations

Journal of Computational Physics

On weighted Hilbert spaces and integration of functions of infinitely many variables

Journal of Complexity