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We consider the use of multipreconditioning to solve linear systems when more than one preconditioner is available but the optimal choice is not known. In particular, we consider a selective multipreconditioned GMRES algorithm where we…
In simulations of fluid motion time accuracy has proven to be elusive. We seek highly accurate methods with strong enough stability properties to deal with the richness of scales of many flows. These methods must also be easy to implement…
We introduce a class of unconditionally energy stable, high order accurate schemes for gradient flows in a very general setting. The new schemes are a high order analogue of the minimizing movements approach for generating a time discrete…
This paper presents a probabilistic perspective on iterative methods for approximating the solution $\mathbf{x}_* \in \mathbb{R}^d$ of a nonsingular linear system $\mathbf{A} \mathbf{x}_* = \mathbf{b}$. In the approach a standard iterative…
Energy system optimization models are increasing in scope and resolution, yielding large and challenging linear programs. For a long time, the standard way to address such problems has relied on shared-memory interior-point methods (IPM),…
Existing computationally efficient methods for penalized likelihood GAM fitting employ iterative smoothness selection on working linear models (or working mixed models). Such schemes fail to converge for a non-negligible proportion of…
This paper aims to understand the relationships among recently developed GPU-accelerated first-order methods (FOMs) for linear programming (LP), with particular emphasis on HPR-LP -- a Halpern Peaceman--Rachford (HPR) method for LP. Our…
Mathematical models for flow and reactive transport in porous media often involve non-linear, degenerate parabolic equations. Their solutions have low regularity, and therefore lower order schemes are used for the numerical approximation.…
An open problem that arises when using modern iterative linear solvers, such as the preconditioned conjugate gradient (PCG) method or Generalized Minimum RESidual method (GMRES) is how to choose the residual tolerance in the linear solver…
Large-scale Gaussian process models are becoming increasingly important and widely used in many areas, such as, computer experiments, stochastic optimization via simulation, and machine learning using Gaussian processes. The standard…
Inference of Large Language Models (LLMs) across computer clusters has become a focal point of research in recent times, with many acceleration techniques taking inspiration from CPU speculative execution. These techniques reduce…
There has been tremendous recent progress on equilibrium-finding algorithms for zero-sum imperfect-information extensive-form games, but there has been a puzzling gap between theory and practice. First-order methods have significantly…
Autoregressive large language models (LLMs) deliver strong performance but require inherently sequential decoding, leading to high inference latency and poor GPU utilization. Speculative decoding mitigates this bottleneck by using a fast…
Recent work has shown that leveraging learned predictions can improve the running time of algorithms for bipartite matching and similar combinatorial problems. In this work, we build on this idea to improve the performance of the widely…
Generalized eigenvalue problems (GEPs) find applications in various fields of science and engineering. For example, principal component analysis, Fisher's discriminant analysis, and canonical correlation analysis are specific instances of…
We propose a new algorithm for solving the graph-fused lasso (GFL), a method for parameter estimation that operates under the assumption that the signal tends to be locally constant over a predefined graph structure. Our key insight is to…
State-of-the-art scene flow algorithms pursue the conflicting targets of accuracy, run time, and robustness. With the successful concept of pixel-wise matching and sparse-to-dense interpolation, we push the limits of scene flow estimation.…
Fluid simulation is an important research topic in computer graphics (CG) and animation in video games. Traditional methods based on Navier-Stokes equations are computationally expensive. In this paper, we treat fluid motion as point cloud…
Numerically solving ordinary differential equations (ODEs) is a naturally serial process and as a result the vast majority of ODE solver software are serial. In this manuscript we developed a set of parallelized ODE solvers using…
In the present work, we study how to develop an efficient solver for the fast resolution of large and sparse linear systems that occur while discretizing elliptic partial differential equations using isogeometric analysis. Our new approach…