On the Spectral Clustering in Algebraic Multigrid Methods

Mathematics > Numerical Analysis [Submitted on 15 Nov 2025 (v1), last revised 3 Jun 2026 (this version, v4)] Title:On the Spectral Clustering in Algebraic Multigrid Methods View PDF HTML (experimental)Abstract:We introduce a new direct multilevel method for solving arbitrary complex square linear systems that uses a regular smoother and an arbitrary but equal number of pre- and post-smoothings. Through careful analysis of the error propagation operator, we cluster the spectrum of this operator. This allows us to write a direct K-cycle version of the method. Submission history From: Jose Pablo Lucero Lorca [view email][v1] Sat, 15 Nov 2025 17:18:22 UTC (193 KB) [v2] Sat, 21 Feb 2026 03:11:05 UTC (294 KB) [v3] Mon, 16 Mar 2026 19:03:09 UTC (294 KB) [v4] Wed, 3 Jun 2026 16:20:01 UTC (290 KB) Current browse context: math.NA References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer (What is the Explorer?) Connected Papers (What is Connected Papers?) Litmaps (What is Litmaps?) scite Smart Citations (What are Smart Citations?) Code, Data and Media Associated with this Article alphaXiv (What is alphaXiv?) CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub (What is DagsHub?) Gotit.pub (What is GotitPub?) Hugging Face (What is Huggingface?) ScienceCast (What is ScienceCast?) Demos Recommenders and Search Tools Influence Flower (What are Influence Flowers?) CORE Recommender (What is CORE?) arXivLabs: experimental projects with community collaborators Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.