Hybrid Dealiasing and Implicit Packing for Real Convolutions

[2608.14497] Hybrid Dealiasing and Implicit Packing for Real Convolutions Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Numerical Analysis arXiv:2608.14497 (math) [Submitted on 14 Aug 2026] Title: Hybrid Dealiasing and Implicit Packing for Real Convolutions Authors: Noel Murasko , John C. Bowman View a PDF of the paper titled Hybrid Dealiasing and Implicit Packing for Real Convolutions, by Noel Murasko and 1 other authors View PDF HTML (experimental) Abstract: Hybrid dealiasing is an FFT-based method for computing linear convolutions of complex-valued data that reduces the cost of dealiasing by performing zero padding implicitly. We develop two new algorithms that extend hybrid dealiasing to real-valued convolutions. The first algorithm exploits conjugate symmetries in the transformed data and computes each residue contribution directly. The second algorithm employs complex-valued hybrid dealiasing via a new implicit packing technique, which packs real-valued data into complex-valued arrays and performs all unpacking and packing operations implicitly in the transformed domain. Multidimensional versions of both algorithms are obtained by recursive decomposition into lower-dimensional convolutions. Based on these algorithms, efficient routines to compute convolutions of equal-length input arrays are implemented in the open-source FFTW++ library. These routines outperform the standard method of explicit zero padding in one, two, and three dimensions. In many cases, implicit packing without hybrid dealiasing is nearly as fast as the general hybrid dealiasing algorithm, particularly when multithreading. Comments: 19 pages, 7 figures Subjects: Numerical Analysis (math.NA) MSC classes: 65T50, 65Y05 Cite as: arXiv:2608.14497 [math.NA] (or arXiv:2608.14497v1 [math.NA] for this version) https://doi.org/10.48550/arXiv.2608.14497 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Noel Murasko [ view email ] [v1] Fri, 14 Aug 2026 17:12:59 UTC (101 KB) Full-text links: Access Paper: View a PDF of the paper titled Hybrid Dealiasing and Implicit Packing for Real Convolutions, by Noel Murasko and 1 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.NA < prev | next > new | recent | 2026-08 Change to browse by: cs cs.NA math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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