Related papers: Accelerating eigenvector and pseudospectra computa…

This paper presents an accelerated quadrature scheme for the evaluation of layer potentials in three dimensions. Our scheme combines a generic, high order quadrature method for singular kernels called Quadrature by Expansion (QBX) with a…

In this paper we describe spectral transformation algorithms for the computation of eigenvalues with positive real part of sparse nonsymmetric matrix pencils $(J,L)$, where $L$ is of the form $\pmatrix{M&0\cr 0&0}$. For this we define a…

Multidimensional imaging, capturing image data in more than two dimensions, has been an emerging field with diverse applications. Due to the limitation of two-dimensional detectors in obtaining the high-dimensional image data, computational…

Spectral clustering is a fundamental technique in the field of data mining and information processing. Most existing spectral clustering algorithms integrate dimensionality reduction into the clustering process assisted by manifold learning…

Achieving completeness in the motion planning problem demands substantial computation power, especially in high dimensions. Recent developments in parallel computing have rendered this more achievable. We introduce an embarrassingly…

Topology optimization problems generally support multiple local minima, and real-world applications are typically three-dimensional. In previous work [I. P. A. Papadopoulos, P. E. Farrell, and T. M. Surowiec, Computing multiple solutions of…

Mixed Boolean-Arithmetic (MBA) obfuscation is a common technique used to transform simple expressions into semantically equivalent but more complex combinations of boolean and arithmetic operators. Its widespread usage in DRM systems,…

We present a simple spectral approach to the well-studied constrained clustering problem. It captures constrained clustering as a generalized eigenvalue problem with graph Laplacians. The algorithm works in nearly-linear time and provides…

We present an eigenspectrum partitioning scheme without inversion for the recently described real-space electronic transport code, TRANSEC. The primary advantage of TRANSEC is its highly parallel algorithm, which enables studying…

We generalize $\epsilon$-pseudospectra and the associated computational algorithms to the generalized eigenvalue problem. Rank one perturbations are used to determine the $\epsilon$-pseudospectra.

An efficient algorithm for computing eigenvectors of a matrix of integers by exact computation is proposed. The components of calculated eigenvectors are expressed as polynomials in the eigenvalue to which the eigenvector is associated, as…

Fairness of decision-making algorithms is an increasingly important issue. In this paper, we focus on spectral clustering with group fairness constraints, where every demographic group is represented in each cluster proportionally as in the…

Sparse linear systems are typically solved using preconditioned iterative methods, but applying preconditioners via sparse triangular solves introduces bottlenecks due to irregular memory accesses and data dependencies. This work leverages…

In this paper, we consider an approach to the parallelizing of the algorithms realizing the modified probability changigng method with adaptation and partial rollback procedure for constrained pseudo-Boolean optimization problems. Existing…

Dedicated hardware accelerators are suitable for parallel computational tasks. Moreover, they have the tendency to accept inexact results. These hardware accelerators are extensively used in image processing and computer vision…

In this paper, we describe and analyze the spectral properties of a number of exact block preconditioners for a class of double saddle point problems. Among all these, we consider an inexact version of a block triangular preconditioner…

It is important to have fast and effective methods for simplifying 3-manifold triangulations without losing any topological information. In theory this is difficult: we might need to make a triangulation super-exponentially more complex…

Specialized function gradient computing hardware could greatly improve the performance of state-of-the-art optimization algorithms, e.g., based on gradient descent or conjugate gradient methods that are at the core of control, machine…

High-performance implementations of graph algorithms are challenging to implement on new parallel hardware such as GPUs because of three challenges: (1) the difficulty of coming up with graph building blocks, (2) load imbalance on parallel…

Numerical simulation of fluids plays an essential role in modeling many physical phenomena, such as weather, climate, aerodynamics and plasma physics. Fluids are well described by the Navier-Stokes equations, but solving these equations at…