2021/02/24 by Alexander Engelmann, Timm Faulwasser, Engelmann, Alexander +1 · 3 citations
Computer Science · Engineering · Mathematics · #A priori and a posteriori #Advanced Adaptive Filtering Techniques #Algorithm #Applied mathematics #Computer science #Conjugate gradient method #Convergence (economics) #Decomposition #Distributed Control Multi-Agent Systems #FOS: Electrical engineering #FOS: Mathematics #Key (lock) #Manifold (fluid mechanics) #Mathematical optimization #Mathematics #Optimization and Control (math.OC) #Rate of convergence #Sparse and Compressive Sensing Techniques #Systems and Control (eess.SY) #cs.SY #eess.SY #electronic engineering #information engineering #math.OC
paper · pdf · doi:10.48550/arxiv.2102.12311
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2021/02/24 · arxiv created 2021/09/02 · arxiv updated 2021/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/08
Solving structured systems of linear equations in a non-centralized fashion is an important step in many distributed optimization and control algorithms. Fast convergence is required in manifold applications. Known decentralized algorithms, however, typically exhibit asymptotic convergence at a linear rate. This note proposes an essentially decentralized variant of the Conjugate Gradient algorithm (d-CG). The proposed method exhibits a practical superlinear convergence rate and comes with a priori computable finite-step convergence guarantees. In contrast to previous works, we consider sum-wise decomposition instead of row-wise decomposition which enables application in multi-agent settings. We illustrate the performance of d-CG on problems from sensor fusion and compare the results to the widely-used Alternating Direction Method of Multipliers.