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Conic optimization is the minimization of a differentiable convex objective function subject to conic constraints. We propose a novel primal-dual first-order method for conic optimization, named proportional-integral projected gradient…
Sensors producing 3D point clouds such as 3D laser scanners and RGB-D cameras are widely used in robotics, be it for autonomous driving or manipulation. Aligning point clouds produced by these sensors is a vital component in such…
We deal with interval parametric systems of linear equations and the goal is to solve such systems, which basically comes down to finding an enclosure for a parametric solution set. Obviously we want this enclosure to be as tight as…
Topology optimization for large scale problems continues to be a computational challenge. Several works exist in the literature to address this topic, and all make use of iterative solvers to handle the linear system arising from the Finite…
Conic optimization is the minimization of a convex quadratic function subject to conic constraints. We introduce a novel first-order method for conic optimization, named \emph{extrapolated proportional-integral projected gradient method…
Principal component analysis (PCA) is a key statistical technique for multivariate data analysis. For large data sets the common approach to PCA computation is based on the standard NIPALS-PCA algorithm, which unfortunately suffers from…
Domain-specific languages that execute image processing pipelineson GPUs, such as Halide and Forma, operate by 1) dividing the image into overlapped tiles, and 2) fusing loops to improve memory locality. However, current approaches have…
In this paper, we consider the dual formulation of minimizing $\sum_{i\in I}f_i(x_i)+\sum_{j\in J} g_j(\mathcal{A}_jx)$ with the index sets $I$ and $J$ being large. To address the difficulties from the high dimension of the variable $x$…
Computing on encrypted data is a promising approach to reduce data security and privacy risks, with homomorphic encryption serving as a facilitator in achieving this goal. In this work, we accelerate homomorphic operations using the…
This paper considers the multi-agent distributed linear least-squares problem. The system comprises multiple agents, each agent with a locally observed set of data points, and a common server with whom the agents can interact. The agents'…
Pulay's Direct Inversion in the Iterative Subspace (DIIS) method is one of the most widely used mixing schemes for accelerating the self-consistent solution of electronic structure problems. In this work, we propose a simple generalization…
Preconditioned Krylov subspace (KSP) methods are widely used for solving large-scale sparse linear systems arising from numerical solutions of partial differential equations (PDEs). These linear systems are often nonsymmetric due to the…
Data augmentation is a crucial step in the development of robust supervised learning models, especially when dealing with limited datasets. This study explores interpolation techniques for the augmentation of geo-referenced data, with the…
The discontinuous Petrov-Galerkin (DPG) methodology of Demkowicz and Gopalakrishnan [15,17] guarantees the optimality of the solution in an energy norm, and provides several features facilitating adaptive schemes. A key question that has…
Accurate simulations are essential for engineering applications, and intricate continuum mechanical material models are constructed to achieve this goal. However, the increasing complexity of the material models and geometrical properties…
This paper presents a scalable physics-based block preconditioner for mixed-dimensional models in beam-solid interaction and their application in engineering. In particular, it studies the linear systems arising from a regularized…
Many processes can correspond to reactive impregnation in porous solids. These processes are usually numerically computed by classical methods like finite element method, finite volume method, etc. The disadvantage of these methods remains…
We establish a new iterative method for solving a class of large and sparse linear systems of equations with three-by-three block coefficient matrices having saddle point structure. Convergence properties of the proposed method are studied…
We present two minimum residual methods for solving sequences of shifted linear systems, the right-preconditioned shifted GMRES and shifted recycled GMRES algorithms which use a seed projection strategy often employed to solve multiple…
We study the interpolation capabilities of implicit neural representations (INRs) of images. In principle, INRs promise a number of advantages, such as continuous derivatives and arbitrary sampling, being freed from the restrictions of a…