相关论文: A reduced fast component-by-component construction…

This paper investigates the construction of space-filling designs for computer experiments. The space-filling property is characterized by the covering and separation radii of a design, which are integrated through the unified criterion of…

In this paper we investigate multivariate integration in weighted unanchored Sobolev spaces of smoothness of arbitrarily high order. As quadrature points we employ higher order polynomial lattice point sets over $\mathbb{F}_{2}$ which are…

Lattice-like structures can provide a combination of high stiffness with light weight that is useful in many applications, but a resolved finite element mesh of such structures results in a computationally expensive discretization. This…

Lattice rules are among the most prominently studied quasi-Monte Carlo methods to approximate multivariate integrals. A rank-$1$ lattice rule to approximate an $s$-dimensional integral is fully specified by its \emph{generating vector}…

Higher order scrambled digital nets are randomized quasi-Monte Carlo rules which have recently been introduced in [J. Dick, Ann. Statist., 39 (2011), 1372--1398] and shown to achieve the optimal rate of convergence of the root mean square…

The star-discrepancy is a quantitative measure for the irregularity of distribution of a point set in the unit cube that is intimately linked to the integration error of quasi-Monte Carlo algorithms. These popular integration rules are…

Lattice-type structures can provide a combination of stiffness with light weight that is desirable in a variety of applications. Design optimization of these structures must rely on approximations of the governing physics to render solution…

We propose a new sparse regression method called the component lasso, based on a simple idea. The method uses the connected-components structure of the sample covariance matrix to split the problem into smaller ones. It then solves the…

We study quasi-Monte Carlo (QMC) methods for numerical integration of multivariate functions defined over the high-dimensional unit cube. Lattice rules and polynomial lattice rules, which are special classes of QMC methods, have been…

In the analysis of using quasi-Monte Carlo (QMC) methods to approximate expectations of a linear functional of the solution of an elliptic PDE with random diffusion coefficient the sensitivity w.r.t. the parameters is often stated in terms…

In this paper, we describe a new algorithm to build a few sparse principal components from a given data matrix. Our approach does not explicitly create the covariance matrix of the data and can be viewed as an extension of the Kogbetliantz…

Higher order digital nets are special classes of point sets for quasi-Monte Carlo rules which achieve the optimal convergence rate for numerical integration of smooth functions. An explicit construction of higher order digital nets was…

This paper presents a generalization of the "weighted least-squares" (WLS), named "weighted pairing least-squares" (WPLS), which uses a rectangular weight matrix and is suitable for data alignment problems. Two fast solving methods,…

We propose a method for crystal structure prediction based on a new structure generation algorithm and on-lattice machine learning interatomic potentials. Our algorithm generates the atomic configurations assigning atomic species to sites…

A classical theorem of Spencer shows that any set system with n sets and n elements admits a coloring of discrepancy O(n^1/2). Recent exciting work of Bansal, Lovett and Meka shows that such colorings can be found in polynomial time. In…

This article presents a simplified formulation for the weak Galerkin finite element method for the Stokes equation without using the degrees of freedom associated with the unknowns in the interior of each element as formulated in the…

In this paper we investigate the benefits of using Z(2)xZ(2) single timeslice stochastic sources for the calculation of light quark physics on the lattice. Meson 2-point correlators measured using sources stochastic in only spin and those…

We show that a very simple randomised algorithm for numerical integration can produce a near optimal rate of convergence for integrals of functions in the $d$-dimensional weighted Korobov space. This algorithm uses a lattice rule with a…

We present a new algorithm for estimating the star discrepancy of arbitrary point sets. Similar to the algorithm for discrepancy approximation of Winker and Fang [SIAM J. Numer. Anal. 34 (1997), 2028--2042] it is based on the optimization…

Discrepancy is a well-known measure for the irregularity of the distribution of a point set. Point sets with small discrepancy are called low-discrepancy and are known to efficiently fill the space in a uniform manner. Low-discrepancy…