Related papers: Random Leja points
This paper presents new fast algorithms for Hermite interpolation and evaluation over finite fields of characteristic two. The algorithms reduce the Hermite problems to instances of the standard multipoint interpolation and evaluation…
Random Ising systems on a general hierarchical lattice with both, random fields and random bonds, are considered. Rigorous inequalities between eigenvalues of the Jacobian renormalization matrix at the pure fixed point are obtained. These…
We develop a novel, fundamental and surprisingly simple randomized iterative method for solving consistent linear systems. Our method has six different but equivalent interpretations: sketch-and-project, constrain-and-approximate, random…
Finding suitable points for multivariate polynomial interpolation and approximation is a challenging task. Yet, despite this challenge, there has been tremendous research dedicated to this singular cause. In this paper, we begin by…
Despite the enormous success of Hamiltonian Monte Carlo and related Markov Chain Monte Carlo (MCMC) methods, sampling often still represents the computational bottleneck in scientific applications. Availability of parallel resources can…
Rounding linear programs using techniques from discrepancy is a recent approach that has been very successful in certain settings. However this method also has some limitations when compared to approaches such as randomized and iterative…
We initiate the study of Local Computation Algorithms on average case inputs. In the Local Computation Algorithm (LCA) model, we are given probe access to a huge graph, and asked to answer membership queries about some combinatorial…
In computational practice, we often encounter situations where only measurements at equally spaced points are available. Using standard polynomial interpolation in such cases can lead to highly inaccurate results due to numerical…
We describe an iterative method to optimize the multi-scale entanglement renormalization ansatz (MERA) for the low-energy subspace of local Hamiltonians on a D-dimensional lattice. For translation invariant systems the cost of this…
Density estimation and inference methods are widely used in empirical work. When the underlying distribution has compact support, conventional kernel-based density estimators are no longer consistent near or at the boundary because of their…
Symbolic data analysis has been proposed as a technique for summarising large and complex datasets into a much smaller and tractable number of distributions -- such as random rectangles or histograms -- each describing a portion of the…
We propose a general framework of iteratively reweighted l1 methods for solving lp regularization problems. We prove that after some iteration k, the iterates generated by the proposed methods have the same support and sign as the limit…
The Lloyd-Max algorithm is a classical approach to perform K-means clustering. Unfortunately, its cost becomes prohibitive as the training dataset grows large. We propose a compressive version of K-means (CKM), that estimates cluster…
By analogy with Monte Carlo algorithms, we propose new strategies for design and redesign of small molecule libraries in high-throughput experimentation, or combinatorial chemistry. Several Monte Carlo methods are examined, including…
There has been significant progress in the study of sampling discretization of integral norms for both a designated finite-dimensional function space and a finite collection of such function spaces (universal discretization). Sampling…
We consider the problem of interpolating an unknown multivariate polynomial with coefficients taken from a finite field or as numerical approximations of complex numbers. Building on the recent work of Garg and Schost, we improve on the…
The popular K-means clustering algorithm potentially suffers from a major weakness for further analysis or interpretation. Some cluster may have disproportionately more (or fewer) points from one of the subpopulations in terms of some…
This paper presents a family of new methods for locating/fitting hyperplanes with respect to a given set of points. We introduce a general framework for a family of aggregation criteria of different distance-based errors. The most popular…
We investigate different geometrical properties of the inhomogeneous Poisson point process $\Lambda_{\mu}$ associated to a positive, locally finite, $\sigma$-finite measure $\mu$ on the unit disk. In particular, we characterize the…
Randomized linear system solvers have become popular as they have the potential to reduce floating point complexity while still achieving desirable convergence rates. One particularly promising class of methods, random sketching solvers,…