D-Index & Metrics Best Publications

D-Index & Metrics

Discipline name D-index D-index (Discipline H-index) only includes papers and citation values for an examined discipline in contrast to General H-index which accounts for publications across all disciplines. Citations Publications World Ranking National Ranking
Mathematics D-index 30 Citations 4,222 125 World Ranking 2232 National Ranking 57

Overview

What is he best known for?

The fields of study he is best known for:

  • Mathematical analysis
  • Algebra
  • Real number

Josef Dick mainly focuses on Rate of convergence, Quasi-Monte Carlo method, Numerical integration, Sobolev space and Discrete mathematics. His studies in Rate of convergence integrate themes in fields like Expected value, Integral equation, Random field and Finite field. His Quasi-Monte Carlo method research includes themes of Unit cube, Applied mathematics and Rank.

In his study, Bounded function is strongly linked to High dimensional, which falls under the umbrella field of Unit cube. His Sobolev space study combines topics in areas such as Sequence and Hilbert space. His Hilbert space research is multidisciplinary, relying on both Function space, Tensor product, Kernel embedding of distributions, Algorithm and Polynomial.

His most cited work include:

  • Digital Nets and Sequences: Discrepancy Theory and Quasi-Monte Carlo Integration (565 citations)
  • High-dimensional integration: The quasi-Monte Carlo way (400 citations)
  • Walsh Spaces Containing Smooth Functions and Quasi-Monte Carlo Rules of Arbitrary High Order (136 citations)

What are the main themes of his work throughout his whole career to date?

Discrete mathematics, Combinatorics, Unit cube, Quasi-Monte Carlo method and Applied mathematics are his primary areas of study. His Discrete mathematics research is multidisciplinary, incorporating elements of Rate of convergence, Polynomial, Bounded function and Lattice. His biological study deals with issues like Sequence, which deal with fields such as Measure.

His research investigates the connection between Combinatorics and topics such as Upper and lower bounds that intersect with problems in Bounded variation and Point. Sobolev space and Hilbert space is closely connected to Function space in his research, which is encompassed under the umbrella topic of Unit cube. His research in Quasi-Monte Carlo method focuses on subjects like Numerical integration, which are connected to Unit sphere and Space.

He most often published in these fields:

  • Discrete mathematics (31.86%)
  • Combinatorics (28.92%)
  • Unit cube (24.51%)

What were the highlights of his more recent work (between 2016-2021)?

  • Unit cube (24.51%)
  • Applied mathematics (22.06%)
  • Quasi-Monte Carlo method (23.53%)

In recent papers he was focusing on the following fields of study:

Josef Dick spends much of his time researching Unit cube, Applied mathematics, Quasi-Monte Carlo method, Polynomial and Discrete mathematics. His Unit cube research includes elements of Function space, Lattice, Lattice, Finite field and Rate of convergence. His Applied mathematics research incorporates themes from Bayes estimator, Cumulative distribution function, Uncertainty quantification, Product measure and Monte Carlo method.

His research in Quasi-Monte Carlo method intersects with topics in Multivariate statistics, Star and Inversive. The Polynomial study combines topics in areas such as Point set and Exponential function. Josef Dick interconnects Dimension and Combinatorics in the investigation of issues within Discrete mathematics.

Between 2016 and 2021, his most popular works were:

  • Multilevel higher-order quasi-Monte Carlo Bayesian estimation (26 citations)
  • Higher order Quasi-Monte Carlo integration for Bayesian PDE Inversion (8 citations)
  • Discrepancy of second order digital sequences in function spaces with dominating mixed smoothness (7 citations)

In his most recent research, the most cited papers focused on:

  • Mathematical analysis
  • Algebra
  • Real number

Josef Dick focuses on Unit cube, Applied mathematics, Quasi-Monte Carlo method, Uncertainty quantification and Polynomial. His biological study spans a wide range of topics, including Rate of convergence, Distribution and Pure mathematics. His Rate of convergence research is multidisciplinary, relying on both Sobol sequence, Algorithm, Lattice and Numerical integration.

His study in Uncertainty quantification is interdisciplinary in nature, drawing from both Bayes estimator, Discretization, Monte Carlo method and Finite element method. Josef Dick works mostly in the field of Polynomial, limiting it down to concerns involving Lattice and, occasionally, Weighted space, Discrete mathematics, Dimension, Concave function and Richardson extrapolation. The Function space study which covers Uniform distribution that intersects with Sobolev space.

This overview was generated by a machine learning system which analysed the scientist’s body of work. If you have any feedback, you can contact us here.

Best Publications

Digital Nets and Sequences: Discrepancy Theory and Quasi-Monte Carlo Integration

Josef Dick;Friedrich Pillichshammer.
(2010)

822 Citations

High-dimensional integration: The quasi-Monte Carlo way

Josef Dick;Frances Y. Kuo;Ian H. Sloan.
Acta Numerica (2013)

549 Citations

Walsh Spaces Containing Smooth Functions and Quasi-Monte Carlo Rules of Arbitrary High Order

Josef Dick.
SIAM Journal on Numerical Analysis (2008)

141 Citations

HIGHER ORDER QMC GALERKIN DISCRETIZATION FOR PARAMETRIC OPERATOR EQUATIONS

Josef Dick;Frances Y. Kuo;Quoc T. Le Gia;Dirk Nuyens.
arXiv: Numerical Analysis (2013)

111 Citations

Good Lattice Rules in Weighted Korobov Spaces with General Weights

Josef Dick;Ian H. Sloan;Xiaoqun Wang;Henryk Woźniakowski.
Numerische Mathematik (2006)

111 Citations

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

Josef Dick;Friedrich Pillichshammer.
Journal of Complexity (2005)

108 Citations

Liberating the weights

Josef Dick;Ian H. Sloan;Xiaoqun Wang;Henryk Woźniakowski.
Journal of Complexity (2004)

100 Citations

Explicit Constructions of Quasi-Monte Carlo Rules for the Numerical Integration of High-Dimensional Periodic Functions

Josef Dick.
SIAM Journal on Numerical Analysis (2007)

93 Citations

Higher Order QMC Petrov--Galerkin Discretization for Affine Parametric Operator Equations with Random Field Inputs

Josef Dick;Frances Y. Kuo;Quoc Thong Le Gia;Dirk Nuyens.
SIAM Journal on Numerical Analysis (2014)

90 Citations

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

Josef Dick.
Journal of Complexity (2004)

86 Citations

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