Related papers: Mixed precision matrix interpolative decomposition…
We propose an extrapolation technique that allows accuracy improvement of the discrete dipole approximation computations. The performance of this technique was studied empirically based on extensive simulations for 5 test cases using many…
Multiple patterning lithography (MPL) is regarded as one of the most promising ways of overcoming the resolution limitations of conventional optical lithography due to the delay of next-generation lithography technology. As the feature size…
This work proposes a mathematically founded mixed precision accumulation strategy for the inference of neural networks. Our strategy is based on a new componentwise forward error analysis that explains the propagation of errors in the…
In recent years, the fervent demand for computational power across various domains has prompted hardware manufacturers to introduce specialized computing hardware aimed at enhancing computational capabilities. Particularly, the utilization…
Recent development on mixed precision techniques has largely enhanced the performance of various linear algebra solvers, one of which being the solver for the least squares problem $\min_{x}\lVert b-Ax\rVert_{2}$. By transforming least…
Compression is a crucial solution for data reduction in modern scientific applications due to the exponential growth of data from simulations, experiments, and observations. Compression with progressive retrieval capability allows users to…
Mixed-precision computations are a hallmark of the current stage of AI, driving the progress in large language models towards efficient, locally deployable solutions. This article addresses the floating-point computation of…
We propose an algorithm for generating explicit solutions of multiparametric mixed-integer convex programs to within a given suboptimality tolerance. The algorithm is applicable to a very general class of optimization problems, but is most…
Hierarchical Matrix (H-matrix) is an approximation technique which splits a target dense matrix into multiple submatrices, and where a selected portion of submatrices are low-rank approximated. The technique substantially reduces both time…
Mixed-precision computing has become increasingly important in modern high-performance computing and machine learning applications. When implementing custom mixed-precision functions -- such as fused operators, optimized GPU kernels, or…
Mixed-precision algorithms have been proposed as a way for scientific computing to benefit from some of the gains seen for artificial intelligence (AI) on recent high performance computing (HPC) platforms. A few applications dominated by…
The classic method for computing the spectral decomposition of a real symmetric matrix, the Jacobi algorithm, can be accelerated by using mixed precision arithmetic. The Jacobi algorithm is aiming to reduce the off-diagonal entries…
The widespread adoption of machine learning algorithms necessitates hardware acceleration to ensure efficient performance. This acceleration relies on custom matrix engines that operate on full or reduced-precision floating-point…
The Strassen algorithm and Winograd's variant accelerate matrix multiplication by using fewer arithmetic operations than standard matrix multiplication. Although many papers have been published to accelerate single- as well as…
Strong gravitational lensing is a powerful probe of cosmology and the dark matter distribution. Efficient lensing software is already a necessity to fully use its potential and the performance demands will only increase with the upcoming…
Modern graphics computing units (GPUs) are designed and optimized to perform highly parallel numerical calculations. This parallelism has enabled (and promises) significant advantages, both in terms of energy performance and calculation. In…
With the recent emergence of mixed precision hardware, there has been a renewed interest in its use for solving numerical linear algebra problems fast and accurately. The solution of total least squares problems, i.e., solving $\min_{E,r}…
The Hadamard decomposition is a powerful technique for data analysis and matrix compression, which decomposes a given matrix into the element-wise product of two or more low-rank matrices. In this paper, we develop an efficient algorithm to…
In this paper, we propose two mixed precision algorithms for Block-Jacobi preconditioner(BJAC): a fixed low precision strategy and an adaptive precision strategy. We evaluate the performance improvement of the proposed mixed precision BJAC…
We propose an adaptive mixed precision and dynamically scaled preconditioned conjugate gradient algorithm (AMP-PCG). It dynamically adjusts the precision for storing vectors and computing, exploiting low precision when appropriate, while…