Related papers: Implementation of the conjugate gradient algorithm…

Conjugate gradient (CG) methods are a class of important methods for solving linear equations and nonlinear optimization problems. In this paper, we propose a new stochastic CG algorithm with variance reduction and we prove its linear…

We present our experience of porting the code used in the wave-packet convergent-close-coupling (WP-CCC) approach to run on NVIDIA V100 and AMD MI250X GPUs. The WP-CCC approach is a method used in the field of ion-atom collision physics to…

Large-scale competitive market equilibrium problems arise in a wide range of important applications, including economic decision-making and intelligent manufacturing. Traditional solution methods, such as interior-point algorithms and…

I review recent machine trends and algorithmic developments for dynamical lattice QCD simulations with the HMC algorithm for Wilson-type fermions. The topics include the trend toward multi-core processors and general purpose GPU (GPGPU)…

Discrete variational methods show excellent performance in numerical simulations of different mechanical systems. In this paper, we introduce an iterative procedure for the solution of discrete variational equations for boundary value…

Connections of the conjugate gradient (CG) method with other methods in computational mathematics are surveyed, including the connections with the conjugate direction method, the subspace optimization method and the quasi-Newton method BFGS…

In this paper, we report a reimplementation of the core algorithms of relativistic coupled cluster theory aimed at modern heterogeneous high-performance computational infrastructures. The code is designed for efficient parallel execution on…

Parallel computing can offer an enormous advantage regarding the performance for very large applications in almost any field: scientific computing, computer vision, databases, data mining, and economics. GPUs are high performance many-core…

We present the Lattice QCD application CL2QCD, which is based on OpenCL and can be utilized to run on Graphic Processing Units as well as on common CPUs. We focus on implementation details as well as performance results of selected…

In this paper we propose a cyclical coordinate descent (CCD) algorithm for solving high dimensional risk parity problems. We show that this algorithm converges and is very fast even with large covariance matrices (n > 500). Comparison with…

Significant obstacles exist in scientific domains including genetics, climate modeling, and astronomy due to the management, preprocess, and training on complicated data for deep learning. Even while several large-scale solutions offer…

The high-performance computing (HPC) landscape is undergoing rapid transformation, with an increasing emphasis on energy-efficient and heterogeneous computing environments. This comprehensive study extends our previous research on SYCL's…

In this paper, we focus on solving a sequence of linear systems with an identical (or similar) coefficient matrix. For this type of problems, we investigate the subspace correction and deflation methods, which use an auxiliary matrix…

This paper presents a comprehensive software stack architecture for integrating quantum computing (QC) capabilities with High-Performance Computing (HPC) environments. While quantum computers show promise as specialized accelerators for…

We present a comparison of several modern C++ libraries providing high-level interfaces for programming multi- and many-core architectures on top of CUDA or OpenCL. The comparison focuses on the solution of ordinary differential equations…

Over the past years GPUs have been successfully applied to the task of inverting the fermion matrix in lattice QCD calculations. Even strong scaling to capability-level supercomputers, corresponding to O(100) GPUs or more has been achieved.…

Heterogeneous computing is the strategy of deploying multiple types of processing elements within a single workflow, and allowing each to perform the tasks to which is best suited. To fully harness the power of heterogeneity, we want to be…

Topological quantum error correction is a milestone in the scaling roadmap of quantum computers, which targets circuits with trillions of gates that would allow running quantum algorithms for real-world problems. The square-lattice surface…

Although the performance of hybrid quantum-classical algorithms is highly dependent on the selection of the classical optimizer and the circuit ansatz, a robust and thorough assessment on-hardware of such features has been missing to date.…

Since the development of the conjugate gradient (CG) method in 1952 by Hestenes and Stiefel, CG, has become an indispensable tool in computational mathematics for solving positive definite linear systems. On the other hand, the conjugate…