Related papers: Least Squares on GPUs in Multiple Double Precision

Block-tridiagonal systems are prevalent in state estimation and optimal control, and solving these systems is often the computational bottleneck. Improving the underlying solvers therefore has a direct impact on the real-time performance of…

Large matrix multiplication is a cornerstone of modern machine learning workloads, yet traditional approaches suffer from cubic computational complexity (e.g., $\mathcal{O}(n^3)$ for a matrix of size $n\times n$). We present Low-Rank GEMM,…

Binary convolutional networks have lower computational load and lower memory foot-print compared to their full-precision counterparts. So, they are a feasible alternative for the deployment of computer vision applications on limited…

Computing on graphics processors is maybe one of the most important developments in computational science to happen in decades. Not since the arrival of the Beowulf cluster, which combined open source software with commodity hardware to…

We investigate the problem of certifying optimality for sparse generalized linear models (GLMs), where sparsity is enforced through a cardinality constraint. While Branch-and-Bound (BnB) frameworks can certify optimality using perspective…

In this paper, we propose a mixed-precision convolution unit architecture which supports different integer and floating point (FP) precisions. The proposed architecture is based on low-bit inner product units and realizes higher precision…

The rapid updates in error-resilient applications along with their quest for high throughput have motivated designing fast approximate functional units for Field-Programmable Gate Arrays (FPGAs). Studies that proposed imprecise functional…

The performance of the Hybrid Monte Carlo algorithm is determined by the speed of sparse matrix-vector multiplication within the context of preconditioned conjugate gradient iteration. We study these operations as implemented for the…

Linear solvers are major computational bottlenecks in a wide range of decision support and optimization computations. The challenges become even more pronounced on heterogeneous hardware, where traditional sparse numerical linear algebra…

Overlays have shown significant promise for field-programmable gate-arrays (FPGAs) as they allow for fast development cycles and remove many of the challenges of the traditional FPGA hardware design flow. However, this often comes with a…

Random sketching is a dimensionality reduction technique that approximately preserves norms and singular values up to some $O(1)$ distortion factor with high probability. The most popular sketches in literature are the Gaussian sketch and…

Graphics Processing Units (GPUs) with high computational capabilities used as modern parallel platforms to deal with complex computational problems. We use this platform to solve large-scale linear programing problems by revised simplex…

Real-time trajectory optimization for nonlinear constrained autonomous systems is critical and typically performed by CPU-based sequential solvers. Specifically, reliance on global sparse linear algebra or the serial nature of dynamic…

Gaussian Process Regression (GPR) is an important type of supervised machine learning model with inherent uncertainty measure in its predictions. We propose a new framework, nuGPR, to address the well-known challenge of high computation…

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…

Efficient mixed-precision matrix multiply accumulate (MMA) operations are critical for accelerating deep learning workloads on GPGPUs. However, existing open-source dot product implementations for Tensor Cores rely on discrete arithmetic…

The Random Phase Approximation (RPA) for correlation energy in the grid-based projector augmented wave (gpaw) code is accelerated by porting to the Graphics Processing Unit (GPU) architecture. The acceleration is achieved by grouping…

We present a set of rules to guide the design of GPU algorithms. These rules are grounded on the principle of reducing waste in GPU utility to achieve good speed up. In accordance to these rules, we propose GPU algorithms for 2D…

Iterative solutions of sparse linear systems and sparse eigenvalue problems have a fundamental role in vital fields of scientific research and engineering. The crucial computing kernel for such iterative solutions is the multiplication of a…

High-level applications, such as machine learning, are evolving from simple models based on multilayer perceptrons for simple image recognition to much deeper and more complex neural networks for self-driving vehicle control systems.The…