Related papers: Implementation of the conjugate gradient algorithm…
Applications in High-Performance Computing (HPC) environments face challenges due to increasing complexity. Among them, the increasing usage of sparse data pushes the limits of data structures and programming models and hampers the…
The Discrete Gabor Transform (DGT) is the most commonly used transform for signal analysis and synthesis using a linear frequency scale. It turns out that the involved operators are rich in structure if one samples the discrete phase space…
The method of nonlinear conjugate gradients (NCG) is widely used in practice for unconstrained optimization, but it satisfies weak complexity bounds at best when applied to smooth convex functions. In contrast, Nesterov's accelerated…
We describe aspects of the Chroma software system for lattice QCD calculations. Chroma is an open source C++ based software system developed using the software infrastructure of the US SciDAC initiative. Chroma interfaces with output from…
The architecture and capabilities of the computers currently in use for large-scale lattice QCD calculations are described and compared. Based on this present experience, possible future directions are discussed.
Nowadays, several industrial applications are being ported to parallel architectures. In fact, these platforms allow acquire more performance for system modelling and simulation. In the electric machines area, there are many problems which…
The runtime of a Lattice QCD simulation is dominated by a small kernel, which calculates the product of a vector by a sparse matrix known as the "Dslash" operator. Therefore, this kernel is frequently optimized for various HPC…
To enable heterogeneous computing systems with autonomous programming and optimization capabilities, we propose a unified, end-to-end, programmable graph representation learning (PGL) framework that is capable of mining the complexity of…
Lattice Quantum Chromodynamics simulations typically spend most of the runtime in inversions of the Fermion Matrix. This part is therefore frequently optimized for various HPC architectures. Here we compare the performance of the Intel Xeon…
This paper presents distributed conjugate gradient algorithms for distributed parameter estimation and spectrum estimation over wireless sensor networks. In particular, distributed conventional conjugate gradient (CCG) and modified…
The geometric multigrid method (GMG) is one of the most efficient solving techniques for discrete algebraic systems arising from elliptic partial differential equations. GMG utilizes a hierarchy of grids or discretizations and reduces the…
We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…
This paper proposes distributed adaptive algorithms based on the conjugate gradient (CG) method and the diffusion strategy for parameter estimation over sensor networks. We present sparsity-aware conventional and modified distributed CG…
Coded computation techniques provide robustness against straggling servers in distributed computing, with the following limitations: First, they increase decoding complexity. Second, they ignore computations carried out by straggling…
Typically, the conjugate gradient (CG) algorithm employs mixed precision and even-odd preconditioning to compute propagators for highly improved staggered quarks (HISQ). This approach suffers from critical slowing down as the light quark…
Solving arithmetic tasks is a simple and fundamental skill, yet modern Large Language Models (LLMs) have great difficulty with them. We introduce the Integrated Gated Calculator (IGC), a module that enables LLMs to perform arithmetic by…
We present Lyncs-API, a Python API for Lattice QCD applications currently under development. Lyncs aims to bring several widely used libraries for Lattice QCD under a common framework. Lyncs flexibly links to libraries for CPUs and GPUs in…
In cryptanalysis, solving the discrete logarithm problem (DLP) is key to assessing the security of many public-key cryptosystems. The index-calculus methods, that attack the DLP in multiplicative subgroups of finite fields, require solving…
We present the first open release of the DCA++ project, a high-performance research software framework to solve quantum many-body problems with cutting edge quantum cluster algorithms. DCA++ implements the dynamical cluster approximation…
The Conjugate Gradient method (CGM) is known to be the fastest generic iterative method for solving linear systems with symmetric sign definite matrices. In this paper, we modify this method so that it could find fundamental solitary waves…