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Parallel implementations of Krylov subspace methods often help to accelerate the procedure of finding an approximate solution of a linear system. However, such parallelization coupled with asynchronous and out-of-order execution often…

Mathematical Software · Computer Science 2023-02-09 Roman Iakymchuk , Jose I. Aliaga

Operator splitting is a popular divide-and-conquer strategy for solving differential equations. Typically, the right-hand side of the differential equation is split into a number of parts that are then integrated separately. Many methods…

Numerical Analysis · Mathematics 2023-08-14 Raymond J. Spiteri , Arash Tavassoli , Siqi Wei , Andrei Smolyakov

Synchronized dual-arm rearrangement is widely studied as a common scenario in industrial applications. It often faces scalability challenges due to the computational complexity of robotic arm rearrangement and the high-dimensional nature of…

Robotics · Computer Science 2024-03-14 Wenhao Li , Shishun Zhang , Sisi Dai , Hui Huang , Ruizhen Hu , Xiaohong Chen , Kai Xu

Enhancing the efficiency of iterative computation on graphs has garnered considerable attention in both industry and academia. Nonetheless, the majority of efforts focus on expediting iterative computation by minimizing the running time per…

Distributed, Parallel, and Cluster Computing · Computer Science 2024-07-23 Yijie Zhou , Shufeng Gong , Feng Yao , Hanzhang Chen , Song Yu , Pengxi Liu , Yanfeng Zhang , Ge Yu , Jeffrey Xu Yu

For Hermitian positive definite linear systems and eigenvalue problems, the eigCG algorithm is a memory efficient algorithm that solves the linear system and simultaneously computes some of its eigenvalues. The algorithm is based on the…

High Energy Physics - Lattice · Physics 2010-02-19 Abdou Abdel-Rehim , Kostas Orginos , Andreas Stathopoulos

This paper proposes improving the solve time of a bootstrap AMG designed previously by the authors. This is achieved by incorporating the information, set of algebraically smooth vectors, generated by the bootstrap algorithm, in a single…

Numerical Analysis · Mathematics 2019-07-11 Pasqua D'Ambra , Panayot S. Vassilevski

Benders decomposition (BD), along with its generalized version (GBD), is a widely used algorithm for solving large-scale mixed-integer optimization problems that arise in the operation of process systems. However, the off-the-shelf…

Optimization and Control · Mathematics 2025-08-12 Zhe Li , Bernard T. Agyeman , Ilias Mitrai , Prodromos Daoutidis

Early scheduling algorithms usually adjusted the clock cycle duration to the execution time of the slowest operation. This resulted in large slack times wasted in those cycles executing faster operations. To reduce the wasted times…

Hardware Architecture · Computer Science 2011-11-09 R. Ruiz-Sautua , M. C. Molina , J. M. Mendias , R. Hermida

A High Performance Computing alternative to traditional Krylov subspace methods, pipelined Krylov subspace solvers offer better scalability in the strong scaling limit compared to standard Krylov subspace methods for large and sparse linear…

Distributed, Parallel, and Cluster Computing · Computer Science 2017-04-25 Siegfried Cools , Wim Vanroose

We present a novel class of methods to compute functions of matrices or their action on vectors that are suitable for parallel programming. Solving appropriate simple linear systems of equations in parallel (or computing the inverse of…

Numerical Analysis · Mathematics 2022-10-10 Sergio Blanes

Bilevel optimization has been widely applied in many important machine learning applications such as hyperparameter optimization and meta-learning. Recently, several momentum-based algorithms have been proposed to solve bilevel optimization…

Machine Learning · Computer Science 2021-12-17 Junjie Yang , Kaiyi Ji , Yingbin Liang

This paper proposes an iterative method to solve Mixed-Integer Optimal Control Problems arising from systems with switched dynamics. The so-called relaxed problem plays a central role within this context. Through a numerical example, it is…

Optimization and Control · Mathematics 2025-12-09 Ramin Abbasi-Esfeden , Wim Van Roy , Jan Swevers

ML(n)BiCGStab is a Krylov subspace method for the solution of large, sparse and non-symmetric linear systems. In theory, it is a method that lies between the well-known BiCGStab and GMRES/FOM. In fact, when n = 1, ML(1)BiCGStab is BiCGStab…

Numerical Analysis · Mathematics 2011-06-21 Man-Chung Yeung

We consider solution of multiply shifted systems of nonsymmetric linear equations, possibly also with multiple right-hand sides. First, for a single right-hand side, the matrix is shifted by several multiples of the identity. Such problems…

Mathematical Physics · Physics 2008-11-26 Dean Darnell , Ronald B. Morgan , Walter Wilcox

We propose Mstab, a novel Krylov subspace recycling method for the iterative solution of sequences of linear systems with fixed system matrix and changing right-hand sides. This new method is a straight and simple generalization of IDRstab.…

Numerical Analysis · Mathematics 2016-04-21 Martin Peter Neuenhofen

A prominent approach to solving combinatorial optimization problems on parallel hardware is Ising machines, i.e., hardware implementations of networks of interacting binary spin variables. Most Ising machines leverage second-order…

Emerging Technologies · Computer Science 2022-12-08 Connor Bybee , Denis Kleyko , Dmitri E. Nikonov , Amir Khosrowshahi , Bruno A. Olshausen , Friedrich T. Sommer

In this paper, we propose a bootstrap method applied to massive data processed distributedly in a large number of machines. This new method is computationally efficient in that we bootstrap on the master machine without over-resampling,…

Machine Learning · Statistics 2020-02-21 Yang Yu , Shih-Kang Chao , Guang Cheng

Geometric numerical integration has recently been exploited to design symplectic accelerated optimization algorithms by simulating the Lagrangian and Hamiltonian systems from the variational framework introduced in Wibisono et al. In this…

Optimization and Control · Mathematics 2023-05-19 Valentin Duruisseaux , Melvin Leok

This paper presents a comprehensive review of techniques proposed in the literature for solving bilevel optimization problems encountered in various real-life applications. Bilevel optimization is an appropriate choice for hierarchical…

Optimization and Control · Mathematics 2025-11-06 Dhaval Pujara , Ankur Sinha

Basing on a modification of the "Dichotomy Algorithm" (Terekhov, 2010), we propose a parallel procedure for solving tridiagonal systems of equations with Toeplitz matrices. Taking the structure of the Toeplitz matrices, we may substantially…

Numerical Analysis · Mathematics 2015-12-15 Andrew V. Terekhov