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The article proposes a Caputo fractional conjugate gradient (CFCG) method for unconstrained optimization problems which is applicable to smooth as well as non-smooth problmes. The proposed method uses a non-adaptive version of the Caputo…

Optimization and Control · Mathematics 2025-12-22 Barsha Shawa , Md Abu Talhamainuddin Ansary

In this paper, we consider the nonconvex quadratically constrained quadratic programming (QCQP) with one quadratic constraint. By employing the conjugate gradient method, an efficient algorithm is proposed to solve QCQP that exploits the…

Optimization and Control · Mathematics 2018-07-17 Akram Taati , Maziar Salahi

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…

Numerical Analysis · Mathematics 2019-12-17 Xuping Zhang , Jiefei Yang , Ziying Liu

A fundamental task in numerical computation is the solution of large linear systems. The conjugate gradient method is an iterative method which offers rapid convergence to the solution, particularly when an effective preconditioner is…

Methodology · Statistics 2018-12-18 Jon Cockayne , Chris Oates , Ilse Ipsen , Mark Girolami

Solving large-scale linear systems problems is a cornerstone in scientific and industrial computing. Classical iterative solvers face increasing difficulty as the number of unknowns becomes large, while fully quantum linear solvers require…

Quantum Physics · Physics 2026-04-14 Shigetora Miyashita , Yoshi-aki Shimada

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…

Pattern Formation and Solitons · Physics 2015-05-13 Taras I. Lakoba

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…

Numerical Analysis · Mathematics 2025-05-06 Alexander Lim , Yang Liu , Fred Roosta

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…

Information Theory · Computer Science 2015-11-23 Rodrigo C. de Lamare

The conjugate gradient (CG) method is widely used for solving nonlinear unconstrained optimization problems because it requires less memory to implement. In this paper, we propose a new parameter of the Dai Liao conjugacy condition of the…

Optimization and Control · Mathematics 2024-12-24 Ahmad Alhawarat

We would like to congratulate the authors of "A Bayesian Conjugate Gradient Method" on their insightful paper, and welcome this publication which we firmly believe will become a fundamental contribution to the growing field of probabilistic…

Computation · Statistics 2019-08-09 Francois-Xavier Briol , Francisco A. Diaz De la O , Peter O. Hristov

A simple alternative to the conjugate gradient(CG) method is presented; this method is developed as a special case of the more general iterated Ritz method (IRM) for solving a system of linear equations. This novel algorithm is not based on…

Numerical Analysis · Computer Science 2019-03-28 Josip Dvornik , Damir Lazarevic , Antonia Jaguljnjak Lazarevic , Marija Demsic

Training and inference in Gaussian processes (GPs) require solving linear systems with $n\times n$ kernel matrices. To address the prohibitive $\mathcal{O}(n^3)$ time complexity, recent work has employed fast iterative methods, like…

Machine Learning · Computer Science 2024-03-12 Kaiwen Wu , Jonathan Wenger , Haydn Jones , Geoff Pleiss , Jacob R. Gardner

The paper develops a technique for solving a linear equation $Ax=b$ with a square and nonsingular matrix $A$, using a decentralized gradient algorithm. In the language of control theory, there are $n$ agents, each storing at time $t$ an…

Systems and Control · Computer Science 2015-09-16 Brian D. O. Anderson , Shaoshuai Mou , A. Stephen Morse , Uwe Helmke

This paper introduces a nonlinear conjugate gradient method (NCGM) for addressing the robust counterpart of uncertain multiobjective optimization problems (UMOPs). Here, the robust counterpart is defined as the minimum across objective-wise…

Optimization and Control · Mathematics 2025-03-04 Shubham Kumar , Nihar Kumar Mahato , Debdas Ghosh

The conjugate gradient method (CG) is typically used with a preconditioner which improves efficiency and robustness of the method. Many preconditioners include parameters and a proper choice of a preconditioner and its parameters is often…

Numerical Analysis · Mathematics 2019-06-04 Alexandr Katrutsa , Mike Botchev , George Ovchinnikov , Ivan Oseledets

Generalized linear mixed models (GLMMs) are a widely used tool in statistical analysis. The main bottleneck of many computational approaches lies in the inversion of the high dimensional precision matrices associated with the random…

Computation · Statistics 2025-10-08 Andrea Pandolfi , Omiros Papaspiliopoulos , Giacomo Zanella

The conjugate gradient (CG) method is a classic Krylov subspace method for solving symmetric positive definite linear systems. We introduce an analogous semi-conjugate gradient (SCG) method for unsymmetric positive definite linear systems.…

Numerical Analysis · Mathematics 2022-06-09 Na Huang , Yu-Hong Dai , Dominique Orban , Michael A Saunders

The problem of optimal precision switching for the conjugate gradient (CG) method applied to sparse linear systems is considered. A sparse matrix is defined as an $n\!\times\!n$ matrix with $m\!=\!O(n)$ nonzero entries. The algorithm first…

Numerical Analysis · Mathematics 2026-03-03 Alexander V. Prolubnikov

Linear solvers are key components in any software platform for scientific and engineering computing. The solution of large and sparse linear systems lies at the core of physics-driven numerical simulations relying on partial differential…

Numerical Analysis · Mathematics 2026-04-16 Massimo Bernaschi , Mauro G. Carrozzo , Alessandro Celestini , Giacomo Piperno , Pasqua D'Ambra

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…

Distributed, Parallel, and Cluster Computing · Computer Science 2016-01-19 R. C. de Lamare