Related papers: Accelerating eigenvector and pseudospectra computa…
Pseudoinverses are ubiquitous tools for handling over- and under-determined systems of equations. For computational efficiency, sparse pseudoinverses are desirable. Recently, sparse left and right pseudoinverses were introduced, using…
In this study, we develop a new parallel algorithm for solving systems of linear algebraic equations with the same block-tridiagonal matrix but with different right-hand sides. The method is a generalization of the parallel dichotomy…
Solving partial differential equations (PDEs) using an annealing-based approach involves solving generalized eigenvalue problems. Discretizing a PDE yields a system of linear equations (SLE). Solving an SLE can be formulated as a general…
Mixed-integer quadratic programs (MIQPs) are a versatile way of formulating vehicle decision making and motion planning problems, where the prediction model is a hybrid dynamical system that involves both discrete and continuous decision…
The computational complexity of naive, sampling-based uncertainty quantification for 3D partial differential equations is extremely high. Multilevel approaches, such as multilevel Monte Carlo (MLMC), can reduce the complexity significantly,…
We present an iterative algorithm for computing an invariant subspace associated with the algebraically smallest eigenvalues of a large sparse or structured Hermitian matrix A. We are interested in the case in which the dimension of the…
This paper proposes a fast multi-band image fusion algorithm, which combines a high-spatial low-spectral resolution image and a low-spatial high-spectral resolution image. The well admitted forward model is explored to form the likelihoods…
Algorithms and implementations for computing the sign function of a triangular matrix are fundamental building blocks in algorithms for computing the sign of arbitrary square real or complex matrices. We present novel recursive and cache…
Although state-of-the-art (SOTA) SAT solvers based on conflict-driven clause learning (CDCL) have achieved remarkable engineering success, their sequential nature limits the parallelism that may be extracted for acceleration on platforms…
We describe the multi-GPU gradient boosting algorithm implemented in the XGBoost library (https://github.com/dmlc/xgboost). Our algorithm allows fast, scalable training on multi-GPU systems with all of the features of the XGBoost library.…
We propose an approximation of nonlinear renewal equations by means of ordinary differential equations. We consider the integrated state, which is absolutely continuous and satisfies a delay differential equation. By applying the…
Sparse linear system solvers are computationally expensive kernels that lie at the heart of numerous applications. This paper proposes a flexible preconditioning framework to substantially reduce the time and energy requirements of this…
In this paper, we explore polynomial accelerators that are well-suited for parallel computations, specifically as smoothers in Algebraic MultiGrid (AMG) preconditioners. These accelerators address a minimax problem, initially formulated in…
Understanding material surfaces and interfaces is vital in applications like catalysis or electronics. By combining energies from electronic structure with statistical mechanics, ab initio simulations can in principle predict the structure…
We develop a multilevel approach to compute approximate solutions to backward differential equations (BSDEs). The fully implementable algorithm of our multilevel scheme constructs sequential martingale control variates along a sequence of…
We present a block lower triangular (BLT) preconditioner to accelerate the convergence of nthe Krylov subspace iterative methods, such as generalized minimal residual (GMRES), for solving a broad class of complex symmetric system of linear…
We give the first approximation algorithm for mixed packing and covering semidefinite programs (SDPs) with polylogarithmic dependence on width. Mixed packing and covering SDPs constitute a fundamental algorithmic primitive with recent…
Nonconvex optimization problems arise in different research fields and arouse lots of attention in signal processing, statistics and machine learning. In this work, we explore the accelerated proximal gradient method and some of its…
While deep learning-based methods have demonstrated outstanding results in numerous domains, some important functionalities are missing. Resolution scalability is one of them. In this work, we introduce a novel architecture, dubbed…
Spatial (dataflow) computer architectures can mitigate the control and performance overhead of classical von Neumann architectures such as traditional CPUs. Driven by the popularity of Machine Learning (ML) workloads, spatial devices are…