Related papers: Quadrature Strategies for Constructing Polynomial …
We consider the problem of approximating an unknown function from point evaluations. This problem is a crucial subproblem in many modern (nonlinear) approximation schemes. When obtaining these point evaluations is costly, minimising the…
In this paper, we focus on the solution of online optimization problems that arise often in signal processing and machine learning, in which we have access to streaming sources of data. We discuss algorithms for online optimization based on…
Matrix multiplication is a fundamental building block for large scale computations arising in various applications, including machine learning. There has been significant recent interest in using coding to speed up distributed matrix…
In the era of big data, one of the key challenges is the development of novel optimization algorithms that can accommodate vast amounts of data while at the same time satisfying constraints and limitations of the problem under study. The…
In this paper, we develop a quadrature framework for large-scale kernel machines via a numerical integration representation. Considering that the integration domain and measure of typical kernels, e.g., Gaussian kernels, arc-cosine kernels,…
As non-institutive polynomial chaos expansion (PCE) techniques have gained growing popularity among researchers, we here provide a comprehensive review of major sampling strategies for the least squares based PCE. Traditional sampling…
Sampling from multimodal distributions is a challenging task in scientific computing. When a distribution has an exact symmetry between the modes, direct jumps among them can accelerate the samplings significantly. However, the…
Subsampling methods aim to select a subsample as a surrogate for the observed sample. As a powerful technique for large-scale data analysis, various subsampling methods are developed for more effective coefficient estimation and model…
In this paper, we study the following robust optimization problem. Given an independence system and candidate objective functions, we choose an independent set, and then an adversary chooses one objective function, knowing our choice. Our…
Improvements in technology lead to increasing availability of large data sets which makes the need for data reduction and informative subsamples ever more important. In this paper we construct $ D $-optimal subsampling designs for…
Binary quadratic programming problems have attracted much attention in the last few decades due to their potential applications. This type of problems are NP-hard in general, and still considered a challenge in the design of efficient…
Quadratically optimized polynomials are described which are useful in multi-bosonic algorithms for Monte Carlo simulations of quantum field theories with fermions. Algorithms for the computation of the coefficients and roots of these…
In this paper we present a convergence rate analysis of inexact variants of several randomized iterative methods. Among the methods studied are: stochastic gradient descent, stochastic Newton, stochastic proximal point and stochastic…
We consider the problem of discretizing one-dimensional, real-valued functions as graphs. The goal is to find a small set of points, from which we can approximate the remaining function values. The method for approximating the unknown…
In this paper, we investigate the randomized algorithms for block matrix multiplication from random sampling perspective. Based on the A-optimal design criterion, the optimal sampling probabilities and sampling block sizes are obtained. To…
We study the systematic numerical approximation of Maxwell's equations in dispersive media. Two discretization strategies are considered, one based on a traditional leapfrog time integration method and the other based on convolution…
This paper investigates the use of stratified sampling as a variance reduction technique for approximating integrals over large dimensional spaces. The accuracy of this method critically depends on the choice of the space partition, the…
The numerical methods for differential equation solution allow obtaining a discrete field that converges towards the solution if the method is applied to the correct problem. Nevertheless, the numerical methods have the restricted class of…
A new method of root finding is formulated that uses a numerical iterative process involving three points. A given function y = f(x) whose roots are desired is fitted and approximated by a polynomial function of the form P(x)= a(x-b)^N that…
The theory of Chebyshev approximation has been extensively studied. In most cases, the optimality conditions are based on the notion of alternance or alternating sequence (that is, maximal deviation points with alternating deviation signs).…