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We propose a new algorithm for the fast solution of large, sparse, symmetric positive-definite linear systems, spaND -- sparsified Nested Dissection. It is based on nested dissection, sparsification and low-rank compression. After…
This article presents a new high-order accurate algorithm for finding a particular solution to a linear, constant-coefficient partial differential equation (PDE) by means of a convolution of the volumetric source function with the Green's…
Pole Expansion and Selected Inversion (PEXSI) is an efficient scheme for evaluating selected entries of functions of large sparse matrices as required e.g. in electronic structure algorithms. We show that the triangular factorizations…
Polarization is a degree of freedom of light carrying important information that is usually absent in intensity and spectral content. Imaging polarimetry is the process of determining the polarization state of light, either partially or…
The well-known discrete Fourier transform (DFT) can easily be generalized to arbitrary nodes in the spatial domain. The fast procedure for this generalization is referred to as nonequispaced fast Fourier transform (NFFT). Various…
Accurate localization is an essential technology for the flexible navigation of robots in large-scale environments. Both SLAM-based and map-based localization will increase the computing load due to the increase in map size, which will…
Previous partial permutation synchronization (PPS) algorithms, which are commonly used for multi-object matching, often involve computation-intensive and memory-demanding matrix operations. These operations become intractable for large…
We describe a method to track particles undergoing large displacements. Starting with a list of particle positions sampled at different time points, we assign particle identities by minimizing the sum across all particles of the trace of…
The state-of-the art proof of a global inf-sup condition on mixed finite element schemes does not allow for an analysis of truly indefinite, second-order linear elliptic PDEs. This paper, therefore, first analyses a nonconforming finite…
In this paper, we propose a model's sparse representation based on reduced mixed generalized multiscale finite element (GMsFE) basis methods for elliptic PDEs with random inputs. Mixed generalized multiscale finite element method (GMsFEM)…
Visual localization has become a key enabling component of many place recognition and SLAM systems. Contemporary research has primarily focused on improving accuracy and precision-recall type metrics, with relatively little attention paid…
We adapt a simplified version of the Multi-Scale Analysis presented in \cite{C11} to multi-particle tight-binding Anderson models. Combined with a recent eigenvalue concentration bound for multi-particle systems \cite{C10}, the new method…
We present an efficient method for computing A-optimal experimental designs for infinite-dimensional Bayesian linear inverse problems governed by partial differential equations (PDEs). Specifically, we address the problem of optimizing the…
Localization in a pre-built map is a basic technique for robot autonomous navigation. Existing mapping and localization methods commonly work well in small-scale environments. As a map grows larger, however, more memory is required and…
Large-scale applications of energy density functional (EDF) methods depend on fast and reliable algorithms to solve the associated non-linear self-consistency problem. When dealing with large single-particle variational spaces, existing…
Accurate and efficient computation of Floquet multipliers and subspaces is essential for analyzing limit cycle in dynamical systems and periodic steady state in Radio Frequency simulation. This problem is typically addressed by solving a…
We identify a new "order parameter" for the disorder driven many-body localization (MBL) transition by leveraging artificial intelligence. This allows us to pin down the transition, as the point at which the physics changes qualitatively,…
We use a bootstrap argument to enhance the eigensystem multiscale analysis, introduced by Elgart and Klein for proving localization for the Anderson model at high disorder. The eigensystem multiscale analysis studies finite volume…
We present two algorithms for large-scale low-rank Euclidean distance matrix completion problems, based on semidefinite optimization. Our first method works by relating cliques in the graph of the known distances to faces of the positive…
We present an efficient computational approach to perform real-space electronic structure calculations using an adaptive higher-order finite-element discretization of Kohn-Sham density-functional theory (DFT). To this end, we develop an…