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Implicit neural representations (INRs) have recently emerged as a powerful tool that provides an accurate and resolution-independent encoding of data. Their robustness as general approximators has been shown in a wide variety of data…
Analyzing high-dimensional data presents challenges due to the "curse of dimensionality'', making computations intensive. Dimension reduction techniques, categorized as linear or non-linear, simplify such data. Non-linear methods are…
Iteratively Re-weighted Least Squares (IRLS) is a method for solving minimization problems involving non-quadratic cost functions, perhaps non-convex and non-smooth, which however can be described as the infimum over a family of quadratic…
We propose HAMSI (Hessian Approximated Multiple Subsets Iteration), which is a provably convergent, second order incremental algorithm for solving large-scale partially separable optimization problems. The algorithm is based on a local…
Implicit methods and GPU parallelization are two distinct yet powerful strategies for accelerating high-order CFD algorithms. However, few studies have successfully integrated both approaches within high-speed flow solvers. The core…
Maximum entropy inference and learning of graphical models are pivotal tasks in learning theory and optimization. This work extends algorithms for these problems, including generalized iterative scaling (GIS) and gradient descent (GD), to…
Methods for solving hyperbolic systems typically depend on unknown ordering (e.g., Gauss-Seidel, or sweep/wavefront/marching methods) to achieve good convergence. For many discretisations, mesh types or decompositions these methods do not…
In this paper we accomplish the development of the fast rank-adaptive solver for tensor-structured symmetric positive definite linear systems in higher dimensions. In [arXiv:1301.6068] this problem is approached by alternating minimization…
We develop a new interior-point method (IPM) for symmetric-cone optimization, a common generalization of linear, second-order-cone, and semidefinite programming. In contrast to classical IPMs, we update iterates with a geodesic of the cone…
A multigrid method is proposed in this paper to solve eigenvalue problems by the finite element method based on the shifted-inverse power iteration technique. With this scheme, solving eigenvalue problem is transformed to a series of…
The aim of this paper is to develop an algebraic multigrid method to solve eigenvalue problems based on the combination of the multilevel correction scheme and the algebraic multigrid method for linear equations. Our approach uses the…
Solving the trust-region subproblem (TRS) plays a key role in numerical optimization and many other applications. Based on a fundamental result that the solution of TRS of size $n$ is mathematically equivalent to finding the rightmost…
Support for lower precision computation is becoming more common in accelerator hardware due to lower power usage, reduced data movement and increased computational performance. However, computational science and engineering (CSE) problems…
The Poisson-Nernst-Planck (PNP) equations are one of the most effective model for describing electrostatic interactions and diffusion processes in ion solution systems, and have been widely used in the numerical simulations of biological…
We present a method for solving nonlinear eigenvalue problems using rational approximation. The method uses the AAA method by Nakatsukasa, S\`{e}te, and Trefethen to approximate the nonlinear eigenvalue problem by a rational eigenvalue…
Incomplete LU factorizations of sparse matrices are widely used as preconditioners in Krylov subspace methods to speed up solving linear systems. Unfortunately, computing the preconditioner itself can be time-consuming and sensitive to…
An implicit neural representation (INR) is a neural network that approximates a spatiotemporal function. Many memory-intensive visualization tasks, including modern 4D CT scanning methods, represent data natively as INRs. While INRs are…
Combinatorial optimization (CO) problems are challenging as the computation time grows exponentially with the input. Graph Neural Networks (GNNs) show promise for researchers in solving CO problems. This study investigates the effectiveness…
This work addresses the issue of large covariance matrix estimation in high-dimensional statistical analysis. Recently, improved iterative algorithms with positive-definite guarantee have been developed. However, these algorithms cannot be…
Large-scale eigenvalue computations on sparse matrices are a key component of graph analytics techniques based on spectral methods. In such applications, an exhaustive computation of all eigenvalues and eigenvectors is impractical and…