A Belgian View on Lattice Rules

article

A lower bound for the number of function evaluations in an error estimate for numerical integration

article

A note on E. Thiémard's algorithm to compute bounds for the star discrepancy

A stable recurrence for the incomplete gamma function with imaginary second argument

A theoretical view on transforming low-discrepancy sequences from a cube to a simplex

Advances in multidimensional integration

Algorithm 720; an algorithm for adaptive cubature over a collection of 3-dimensional simplices

article published in 1993

Algorithm 764: Cubpack++

scientific article published on 27 July 2002

Algorithm 824

article

Algorithm 858

scientific article published on 16 January 2007

An adaptive approach to cube-based quasi-Monte Carlo integration on

An adaptive numerical cubature algorithm for simplices

An embedded pair of cubature formulae of degree 5 and 7 for the triangle

An encyclopaedia of cubature formulas

article

An imbedded family of cubature formulae for n-dimensional product regions

Another step forward in searching for cubature formulae with a minimal number of knots for the square

article by R. Cools & Ann Haegemans published June 1988 in Computing

Automatic computation of knots and weights of cubature formulae for circular symmetric planar regions

CHEBINT

Chebyshev lattices, a unifying framework for cubature with Chebyshev weight function

Computational investigations of scrambled Faure sequences

Computing zeros of analytic mappings: A logarithmic residue approach

article

Conditional Sampling for Barrier Option Pricing Under the Heston Model

Conditional Sampling for Barrier Option Pricing under the LT Method

Constructing Embedded Lattice Rules for Multivariate Integration

Constructing cubature formulae: the science behind the art

Constructing lattice rules based on weighted degree of exactness and worst case error

Construction of fully symmetric cubature formulae of degree 4k − 3 for fully symmetric planar regions

Constructions of copy rules

Cubature Formulas of a Nonalgebraic Degree of Precision

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Cubature formulae and orthogonal polynomials

Decomposing the Secondary Cayley Polytope

article published in 2000

Different Quality Indexes for Lattice Rules

Extended exponentially fitted interpolation formulas for oscillatory functions

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Extended quadrature rules for oscillatory integrands

Extensions of Fibonacci Lattice Rules

Extrapolation and Adaptivity in Software for Automatic Numerical Integration on a Cube

Extremal lattices and the construction of lattice rules

FRONT MATTER

Fast Component-by-Component Construction, a Reprise for Different Kernels

Fast algorithms for component-by-component construction of rank-$1$ lattice rules in shift-invariant reproducing kernel {H}ilbert spaces

scholarly article by Dirk Nuyens & Ronald Cools published 4 January 2006 in Mathematics of Computation

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

Five- and six-dimensional lattice rules generated by structured matrices

Good permutations for deterministic scrambled Halton sequences in terms of L 2 -discrepancy

Higher Order Quasi-Monte Carlo Methods: A Comparison

Homotopies Exploiting Newton Polytopes for Solving Sparse Polynomial Systems

In Search for Good Chebyshev Lattices

Integrating products of Bessel functions with an additional exponential or rational factor

Mean-field theory for the Q-state Potts-glass neural network with biased patterns

article

Minimal cubature formulae of degree 2k−1 for two classical functionals

Minimal cubature formulae of trigonometric degree

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Minimizing the L 2 and L ∞ star discrepancies of a single point in the unit hypercube

Minimum classification error training in example based speech and pattern recognition using sparse weight matrices

scholarly article by Mike Matton et al published June 2010 in Journal of Computational and Applied Mathematics

Mixed-volume computation by dynamic lifting applied to polynomial system solving

Monomial cubature rules since “Stroud”: a compilation

Monomial cubature rules since “Stroud”: a compilation — part 2

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Nonlinear reduction for solving deficient polynomial systems by continuation methods

scholarly article by Jan Verschelde & Ronald Cools published December 1992 in Numerische Mathematik

Note on ``Electromagnetic Response of a Large Circular Loop Source on a Layered Earth: A New Computation Method'' by N. P. Singh and T. Mogi

Numerical integration in logistic-normal models

On Generalized Gaussian Quadrature Rules for Singular and Nearly Singular Integrals

On cubature formulae of degree 4k+1 attaining M�ller's lower bound for integrals with circular symmetry

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On obtaining higher order convergence for smooth periodic functions

On obtaining quadratic and cubic error convergence using weighted Kronecker-sequences

On the (non)-existence of some cubature formulas: gaps between a theory and its applications

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On the construction of multi-dimensional embedded cubature formulae

scholarly article by Ronald Cools & Ann Haegemans published November 1989 in Numerische Mathematik

On the convergence of quasi-random sampling importance resampling

On the convergence of quasi-random sampling/importance resampling

article published in 2010

Optimal addition of knots to cubature formulae for planar regions

article

Proof of a conjectured asymptotic expansion for the approximation of surface integrals

Quadrature rules using first derivatives for oscillatory integrands

Quasi-random integration in high dimensions

Recent topics in numerical integration

Reconstruction and Collocation of a Class of Non-periodic Functions by Sampling Along Tent-Transformed Rank-1 Lattices

Rotation invariant cubature formulas over the n-dimensional unit cube

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Smolyak's Construction of Cubature Formulas of Arbitrary Trigonometric Degree

article

Spherical Product Algorithms and the Integration of Smooth Functions with One Singular Point

Symbolic homotopy construction

Symmetric homotopy construction

Template-Based Continuous Speech Recognition

scholarly article by Mathias De Wachter et al published May 2007 in IEEE Transactions on Audio Speech and Language Processing

Tent-transformed lattice rules for integration and approximation of multivariate non-periodic functions ⬇️

scholarly article by Ronald Cools et al published October 2016 in Journal of Complexity

The Birth of Numerical Analysis

The Newton‐Raphson method

The construction of cubature formulae for a family of integrals: A bifurcation problem

The role of embedded integration rules in Bayesian statistics

Three- and four-dimensional $K$-optimal lattice rules of moderate trigonometric degree

Transforming low-discrepancy sequences from a cube to a simplex

Using Box-Muller with Low Discrepancy Points

Why do so many cubature formulae have so many positive weights?