Related papers: Boosting the Efficiency of the Differential Algebr…

We consider large linear and nonlinear fixed point problems, and solution with proximal algorithms. We show that there is a close connection between two seemingly different types of methods from distinct fields: 1) Proximal iterations for…

Fast multipole methods (FMM) were originally developed for accelerating $N$-body problems for particle-based methods. FMM is more than an $N$-body solver, however. Recent efforts to view the FMM as an elliptic Partial Differential Equation…

We present tests of comparison between our versions of the Fast Multipole Algorithm (FMA) and ``classic'' tree-code to evaluate gravitational forces in particle systems. We have optimized the Greengard's original version of FMA allowing for…

Dynamic causal modeling (DCM) is a Bayesian framework to infer directed connections between compartments, and has been used to describe the interactions between underlying neural populations based on functional neuroimaging data. DCM is…

We propose a novel algorithm for supervised dimensionality reduction named Manifold Partition Discriminant Analysis (MPDA). It aims to find a linear embedding space where the within-class similarity is achieved along the direction that is…

We introduce the Fast Free Memory method (FFM), a new fast method for the numerical evaluation of convolution products. Inheriting from the Fast Multipole Method, the FFM is a descent-only and kernel-independent algorithm. We give the…

In a number of problems in computational physics, a finite sum of kernel functions centered at $N$ particle locations located in a box in three dimensions must be extended by imposing periodic boundary conditions on box boundaries. Even…

Functional data analysis (FDA) is an important modern paradigm for handling infinite-dimensional data. An important task in FDA is model-based clustering, which organizes functional populations into groups via subpopulation structures. The…

The derivative-free projection method (DFPM) is an efficient algorithm for solving monotone nonlinear equations. As problems grow larger, there is a strong demand for speeding up the convergence of DFPM. This paper considers the application…

The persistence diagram, which describes the topological features of a dataset, is a key descriptor in Topological Data Analysis. The "Discrete Morse Sandwich" (DMS) method has been reported to be the most efficient algorithm for computing…

This paper introduces a versatile approach for computing the risk of collision specifically tailored for scenarios featuring low relative encounter velocities, but with potential applicability across a wide range of situations. The…

The distributed adaptive signal fusion (DASF) framework allows to solve spatial filtering optimization problems in a distributed and adaptive fashion over a bandwidth-constrained wireless sensor network. The DASF algorithm requires each…

There is an ongoing effort to develop tools that apply distributed computational resources to tackle large problems or reduce the time to solve them. In this context, the Alternating Direction Method of Multipliers (ADMM) arises as a method…

In this paper, we propose a fast multipole method (FMM) for 3-D linearized Poisson-Boltzmann (PB) equation in layered media. The main framework of the algorithm is analogous to the FMM for Helmholtz and Laplace equation in layered media…

A low-latency and energy-efficient tensor algebra accelerator design must optimize how data movement and operations are scheduled (i.e., mapped) in the accelerator architecture. A key mapping optimization is fusion, meaning holding data…

While fast multipole methods (FMMs) are in widespread use for the rapid evaluation of potential fields governed by the Laplace, Helmholtz, Maxwell or Stokes equations, their coupling to high-order quadratures for evaluating layer potentials…

Optimal transmission switching (OTS) improves optimal power flow (OPF) by selectively opening transmission lines, but its mixed-integer formulation increases computational complexity, especially on large grids. To deal with this, we propose…

Symbolic encoding has been used in multi-operator learning as a way to embed additional information for distinct time-series data. For spatiotemporal systems described by time-dependent partial differential equations, the equation itself…

Exascale systems are predicted to have approximately one billion cores, assuming Gigahertz cores. Limitations on affordable network topologies for distributed memory systems of such massive scale bring new challenges to the current parallel…

Coupled matrix and tensor factorizations (CMTF) are frequently used to jointly analyze data from multiple sources, also called data fusion. However, different characteristics of datasets stemming from multiple sources pose many challenges…