Related papers: Efficient Mixed-Precision Matrix Factorization of …
We propose a hyperpower iteration for numerical computation of the outer generalized inverse of a matrix which achieves the 18th order of convergence by using only seven matrix multiplication per iteration loop. This is the record high…
This study explores the use of INT8-based emulation for accelerating traditional FP64-based HPC workloads on modern GPU architectures. Through SCILIB-Accel automatic BLAS offload tool for cache-coherent Unified Memory Architecture, we…
In this work, we propose an architecture and methodology to design hardware/software systems for high-performance embedded computing on FPGA. The hardware side is based on a many-core architecture whose design is generated automatically…
Recent hardware-aware matrix-free algorithms for higher-order finite-element (FE) discretized matrix-vector multiplications reduce floating point operations and data access costs compared to traditional sparse matrix approaches. This work…
The Schur decomposition of a square matrix $A$ is an important intermediate step of state-of-the-art numerical algorithms for addressing eigenvalue problems, matrix functions, and matrix equations. This work is concerned with the following…
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…
Sparse matrix factorization is a popular tool to obtain interpretable data decompositions, which are also effective to perform data completion or denoising. Its applicability to large datasets has been addressed with online and randomized…
Approximate computing has shown to provide new ways to improve performance and power consumption of error-resilient applications. While many of these applications can be found in image processing, data classification or machine learning, we…
The problem is to evaluate a polynomial in several variables and its gradient at a power series truncated to some finite degree with multiple double precision arithmetic. To compensate for the cost overhead of multiple double precision and…
In this paper we propose a fast optimization algorithm for approximately minimizing convex quadratic functions over the intersection of affine and separable constraints (i.e., the Cartesian product of possibly nonconvex real sets). This…
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 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…
Matrix multiplication optimization remains a fundamental challenge in computational mathematics. This work introduces a novel approach that discovers matrix multiplication schemes whose coefficients are restricted to the set $\{-1, 0, 1\}$…
This work proposes a GPU tensor core approach that encodes the arithmetic reduction of $n$ numbers as a set of chained $m \times m$ matrix multiply accumulate (MMA) operations executed in parallel by GPU tensor cores. The asymptotic running…
Mixed-precision Deep Neural Networks achieve the energy efficiency and throughput needed for hardware deployment, particularly when the resources are limited, without sacrificing accuracy. However, the optimal per-layer bit precision that…
In recent years, there is a surge on machine learning applications in industry. Many of them are based on popular AI frameworks like Tensorflow, Torch, Caffe, or MxNet, etc, and are enpowered by accelerator platforms such as GPUs. One…
We present an algorithm to reduce the computational effort for the multiplication of a given matrix with an unknown column vector. The algorithm decomposes the given matrix into a product of matrices whose entries are either zero or integer…
Sketching-based preconditioners have been shown to accelerate the solution of dense least-squares problems with coefficient matrices having substantially more rows than columns. The cost of generating these preconditioners can be reduced by…
This study presents a novel mixed-precision iterative refinement algorithm, GADI-IR, within the general alternating-direction implicit (GADI) framework, designed for efficiently solving large-scale sparse linear systems. By employing…
As CMOS scaling reaches its technological limits, a radical departure from traditional von Neumann systems, which involve separate processing and memory units, is needed in order to significantly extend the performance of today's computers.…