Related papers: Extension and optimization of the FIND algorithm: …
Thanks to their universal approximation properties and new efficient training strategies, Deep Neural Networks are becoming a valuable tool for the approximation of mathematical operators. In the present work, we introduce Mesh-Informed…
In inverting large sparse matrices, the key difficulty lies in effectively exploiting sparsity during the inversion process. One well-established strategy is the nested dissection, which seeks the so-called sparse Cholesky factorization. We…
Over the past decade, reflection matrix microscopy (RMM) and advanced image reconstruction algorithms have emerged to address the fundamental imaging depth limitations of optical microscopy in thick biological tissues and complex media. In…
Path finding algorithm addresses problem of finding shortest path from source to destination avoiding obstacles. There exist various search algorithms namely A*, Dijkstra's and ant colony optimization. Unlike most path finding algorithms…
A cumbersome operation in numerical analysis and linear algebra, optimization, machine learning and engineering algorithms; is inverting large full-rank matrices which appears in various processes and applications. This has both numerical…
Deep representation learning has become one of the most widely adopted approaches for visual search, recommendation, and identification. Retrieval of such representations from a large database is however computationally challenging.…
Second-order Newton-type algorithms that leverage the exact Hessian or its approximation are central to solve nonlinear optimization problems. However, their applications in solving large-scale nonconvex problems are hindered by three…
Linear computation coding is concerned with the compression of multidimensional linear functions, i.e. with reducing the computational effort of multiplying an arbitrary vector to an arbitrary, but known, constant matrix. This paper…
This paper initiates the study of I/O algorithms (minimizing cache misses) from the perspective of fine-grained complexity (conditional polynomial lower bounds). Specifically, we aim to answer why sparse graph problems are so hard, and why…
We consider fast deterministic algorithms to identify the "best" linearly independent terms in multivariate mixtures and use them to compute, up to a user-selected accuracy, an equivalent representation with fewer terms. One algorithm…
In this paper we explore a symmetry-based search space reduction technique which can speed up optimal pathfinding on undirected uniform-cost grid maps by up to 38 times. Our technique decomposes grid maps into a set of empty rectangles,…
During recent decades, there has been a substantial development in optimal mass transport theory and methods. In this work, we consider multi-marginal problems wherein only partial information of each marginal is available, which is a setup…
We provide theoretical analyses for two algorithms that solve the regularized optimal transport (OT) problem between two discrete probability measures with at most $n$ atoms. We show that a greedy variant of the classical Sinkhorn…
Conventional deep convolutional neural networks (CNNs) apply convolution operators uniformly in space across all feature maps for hundreds of layers - this incurs a high computational cost for real-time applications. For many problems such…
This paper presents a novel {\em Interpolated Factored Green Function} method (IFGF) for the accelerated evaluation of the integral operators in scattering theory and other areas. Like existing acceleration methods in these fields, the IFGF…
The Bin Packing Problem is one of the most important optimization problems. In recent years, due to its NP-hard nature, several approximation algorithms have been presented. It is proved that the best algorithm for the Bin Packing Problem…
A new approximate computational framework is proposed for computing the non-equilibrium charge density in the context of the non-equilibrium Green's function (NEGF) method for quantum mechanical transport problems. The framework consists of…
Neural networks have recently gained attention in solving inverse problems. One prominent methodology are Physics-Informed Neural Networks (PINNs) which can solve both forward and inverse problems. In the paper at hand, full waveform…
Numerical simulations including magnetic fields have become important in many fields of astrophysics. Evolution of magnetic fields by the constrained transport algorithm preserves magnetic divergence to machine precision, and thus…
Quantum computation offers a promising alternative to classical computing methods in many areas of numerical science, with algorithms that make use of the unique way in which quantum computers store and manipulate data often achieving…