Skip to content
DraconiticResearch
Search Sources API
220,411 studies31 sourcesUpdated 51 min ago
PreprintCC BY-NC-ND 4.0arXiv

Another Multivector Inverse Algorithm

  • David Arthur Jones
Open at sourcePDFDOICite

Abstract

A numerical algorithm is described for computing the inverse of a non-singular multivector across dimensions. The method wraps a reversion-like product around a Faddeev--LeVerrier--Souriau (FLS) polynomial core. While FLS provides dimensional extensibility, the wrapper reduces the polynomial order of the FLS method, and introduces a sparse multivector which can be further exploited. The construction and essential properties of the initial involution are explained. For dimensions 4--7, the optimized inverse requires fewer real multiplications than a same-dimension multivector product. Dimensions 8--11 follow easily on common hardware with similar efficiency. For dimensions 12--15, higher-precision arithmetic demonstrates the generality of the algorithm when the arithmetic can support it. Performance on common hardware is reported. Directions are included for obtaining a Python package with examples for numerical computation in Clifford algebra, supporting arbitrary signatures including degenerate cases.

Related

  1. Another proof of the U4(Fpn)-inverse theorem
    Sarah Peluse
    arXivPreprintarXiv licenceFull textAlgebra & number theoryCombinatorics & discrete mathematicsarXiv
  2. A Model-Informed Deep Learning Algorithm for Solving the Phaseless Inverse Scattering Problem
    Dinh-Liem Nguyen, Nhung H. Nguyen, Aravinth Ravi
    arXivPreprintCC BY 4.0Full textNumerical analysis & scientific computingarXiv
  3. A tool for new Hybrid models: a swift algorithm to calculate the left inverse of a square root of a horizontally localized climatological ensemble covariance matrix
    Francesco Sardelli, Craig Huntly Bishop
    arXivPreprintarXiv licenceFull textAtmospheric science & meteorologyStatisticsarXiv
  4. Yet Another Family of Complex Structures on S6
    Wenfei Liu, Sönke Rollenske
    arXivPreprintarXiv licenceFull textAlgebra & number theoryGeometry & topologyarXiv
  5. Yet another asymptotic formula for implied volatility
    Masaaki Fukasawa
    arXivPreprintarXiv licenceFull textProbabilityarXiv

Cite

BibTeXRIS
BibTeX
@misc{jones2026another,
  title = {{Another Multivector Inverse Algorithm}},
  author = {David Arthur Jones},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.14549},
  eprint = {2611.14549},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.14549},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Another Multivector Inverse Algorithm
AU  - David Arthur Jones
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.14549
UR  - https://arxiv.org/abs/2611.14549
AB  - A numerical algorithm is described for computing the inverse of a non-singular multivector across dimensions. The method wraps a reversion-like product around a Faddeev--LeVerrier--Souriau (FLS) polynomial core. While FLS provides dimensional extensibility, the wrapper reduces the polynomial order of the FLS method, and introduces a sparse multivector which can be further exploited. The construction and essential properties of the initial involution are explained. For dimensions 4--7, the optimized inverse requires fewer real multiplications than a same-dimension multivector product. Dimensions 8--11 follow easily on common hardware with similar efficiency. For dimensions 12--15, higher-precision arithmetic demonstrates the generality of the algorithm when the arithmetic can support it. Performance on common hardware is reported. Directions are included for obtaining a Python package with examples for numerical computation in Clifford algebra, supporting arbitrary signatures including degenerate cases.
ER  -