Related papers: Leveraging Mixed Precision in Exponential Time Int…
The Paterson--Stockmeyer method is an evaluation scheme for matrix polynomials with scalar coefficients that arise in many state-of-the-art algorithms based on polynomial or rational approximation, for example, those for computing…
Mixture models are a fundamental tool in applied statistics and machine learning for treating data taken from multiple subpopulations. The current practice for estimating the parameters of such models relies on local search heuristics…
With the emergence of mixed precision capabilities in hardware, iterative refinement schemes for solving linear systems $Ax=b$ have recently been revisited and reanalyzed in the context of three or more precisions. These new analyses show…
This study investigates the iterative refinement method applied to the solution of linear discrete inverse problems by considering its application to the Tikhonov problem in mixed precision. Previous works on mixed precision iterative…
In this paper, we implement exponential integrators, specifically Integrating Factor (IF) and Exponential Time Differencing (ETD) methods, using pseudo-spectral techniques to solve phase-field equations within a Python framework. These…
In the present paper, we propose Krylov-based methods for solving large-scale differential Sylvester matrix equations having a low rank constant term. We present two new approaches for solving such differential matrix equations. The first…
The goal of this paper is to present two algorithms for solving systems of inclusion problems, with all component of the systems being a sum of two maximal monotone operators. The algorithms are variants of the forward-backward splitting…
We consider stochastic optimization problems where data is drawn from a Markov chain. Existing methods for this setting crucially rely on knowing the mixing time of the chain, which in real-world applications is usually unknown. We propose…
With growing demand for time-domain simulations of correlated many-body systems, the development of efficient and stable integration schemes for the time-dependent Schr\"odinger equation is of keen interest in modern electronic structure…
Suitable discretizations through tensor product formulas of popular multidimensional operators (diffusion or diffusion--advection, for instance) lead to matrices with $d$-dimensional Kronecker sum structure. For evolutionary Partial…
Large neural networks spend most computation on floating point tensor multiplications. In this work, we find that a floating point multiplier can be approximated by one integer adder with high precision. We propose the linear-complexity…
In this paper, we introduce novel fast matrix inversion algorithms that leverage triangular decomposition and recurrent formalism, incorporating Strassen's fast matrix multiplication. Our research places particular emphasis on triangular…
We present new algorithms to detect and correct errors in the product of two matrices, or the inverse of a matrix, over an arbitrary field. Our algorithms do not require any additional information or encoding other than the original inputs…
In this paper we propose a mixed precision algorithm in the context of the semi-Lagrangian discontinuous Galerkin method. The performance of this approach is evaluated on a traditional dual socket workstation as well as on a Xeon Phi and an…
We propose two methods to find a proper shift parameter in the shift-and-invert method for computing matrix exponential matrix-vector products. These methods are useful in the case of matrix exponential action has to be computed for a…
The explosive demand for artificial intelligence (AI) workloads has led to a significant increase in silicon area dedicated to lower-precision computations on recent high-performance computing hardware designs. However, mixed-precision…
In recent years, accelerated extra-gradient methods have attracted much attention by researchers, for solving monotone inclusion problems. A limitation of most current accelerated extra-gradient methods lies in their direct utilization of…
With the increasing complexity of machine learning models, managing computational resources like memory and processing power has become a critical concern. Mixed precision techniques, which leverage different numerical precisions during…
We report an accessible and robust tool for evaluating the effects of Coulomb collisions on a test particle in a plasma that obeys Maxwell-J\"uttner statistics. The implementation is based on the Beliaev-Budker collision integral which…
This paper presents a new strategy to deal with the excessive diffusion that standard finite volume methods for compressible Euler equations display in the limit of low Mach number. The strategy can be understood as using centered…