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Matrix factorization is a popular approach to solving matrix estimation problems based on partial observations. Existing matrix factorization is based on least squares and aims to yield a low-rank matrix to interpret the conditional sample…
Krylov methods rely on iterated matrix-vector products $A^k u_j$ for an $n\times n$ matrix $A$ and vectors $u_1,\ldots,u_m$. The space spanned by all iterates $A^k u_j$ admits a particular basis -- the \emph{maximal Krylov basis} -- which…
Large scale grid expansion planning studies are essential to rapidly and efficiently decarbonizing the electricity sector. These studies help policy makers and grid participants understand which renewable generation, storage, and…
The shift towards clean energy brings about notable transformations to the energy system. In order to optimally plan a future energy system, it is necessary to consider the influence of several sectors as well as the interaction of the…
The automatic selection of an appropriate time step size has been considered extensively in the literature. However, most of the strategies developed operate under the assumption that the computational cost (per time step) is independent of…
The anisotropic diffusion equation is imperative in understanding cosmic ray diffusion across the Galaxy, the heliosphere, and its interplay with the ambient magnetic field. This diffusion term contributes to the highly stiff nature of the…
Nesterov's well-known scheme for accelerating gradient descent in convex optimization problems is adapted to accelerating stationary iterative solvers for linear systems. Compared with classical Krylov subspace acceleration methods, the…
Upcoming Large Scale Structure surveys aim to achieve an unprecedented level of precision in measuring galaxy clustering. However, accurately modeling these statistics may require theoretical templates that go beyond second-order…
We propose a flexible and theoretically supported framework for scalable nonnegative matrix factorization. The goal is to find nonnegative low-rank components directly from compressed measurements, accessing the original data only once or…
The development of algorithms for enhancing the resilience and efficiency of the power grid requires performance evaluation with real topologies of power transmission networks. However, due to security reasons, such topologies and…
Boundary element methods produce dense linear systems that can be accelerated via multipole expansions. Solved with Krylov methods, this implies computing the matrix-vector products within each iteration with some error, at an accuracy…
The computational efficiency of stochastic simulation algorithms is notoriously limited by the kinetic trapping of the simulated trajectories within low energy basins. Here we present a new method that overcomes kinetic trapping while still…
We present variants of the Conjugate Gradient (CG), Conjugate Residual (CR), and Generalized Minimal Residual (GMRES) methods which are both pipelined and flexible. These allow computation of inner products and norms to be overlapped with…
Exponential is a basic signal form, and how to fast acquire this signal is one of the fundamental problems and frontiers in signal processing. To achieve this goal, partial data may be acquired but result in the severe artifacts in its…
The energy transition, crucial for tackling the climate crisis, demands integrating numerous distributed, renewable energy sources into existing grids. Along with climate change and consumer behavioral changes, this leads to changes and…
Analyzing massive spatial datasets using Gaussian process model poses computational challenges. This is a problem prevailing heavily in applications such as environmental modeling, ecology, forestry and environmental heath. We present a…
In this paper, two efficient iterative algorithms based on the simpler GMRES method are proposed for solving shifted linear systems. To make full use of the shifted structure, the proposed algorithms utilizing the deflated restarting…
In this paper, we propose a novel adaptive-rank method for simulating multi-scale BGK equations, based on a greedy sampling strategy. The method adaptively selects important rows and columns of the solution matrix and updates them using a…
We present a simple and efficient technique in ab initio electronic-structure calculation utilizing real-space double-grid with a high density of grid points in the vicinity of nuclei. This technique promises to greatly reduce the overhead…
We describe a set of network analysis methods based on the rows of the Krylov subspace matrix computed from a network adjacency matrix via power iteration using a non-random initial vector. We refer to these node-specific row vectors as…