PreprintarXiv licencearXiv
The tubal Arnoldi method for tensor function approximation
Abstract
This paper describes Krylov subspace methods based on the tensor t-product for approximating quantities associated with third-order tensor functions. Specifically, it introduces the tensor-tubal Arnoldi method, which projects highdimensional tensor problems onto lower-dimensional tensor Krylov subspaces. The derived method exploits novel algebraic properties of the t-product to address large-scale tensor computations efficiently. Applications include the evaluation of parameter-dependent tensor functions and the solution of multidimensional ordinary differential equations. Numerical experiments illustrate the effectiveness and accuracy of the proposed methods compared with other approaches.
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BibTeX
@misc{bouyghf2026tubal,
title = {{The tubal Arnoldi method for tensor function approximation}},
author = {Fatima Bouyghf and Mohamed El Ghomari and Alaa El Ichi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.11369},
eprint = {2609.11369},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.11369},
}
RIS
TY - UNPB
TI - The tubal Arnoldi method for tensor function approximation
AU - Fatima Bouyghf
AU - Mohamed El Ghomari
AU - Alaa El Ichi
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.11369
UR - https://arxiv.org/abs/2609.11369
AB - This paper describes Krylov subspace methods based on the tensor t-product for approximating quantities associated with third-order tensor functions. Specifically, it introduces the tensor-tubal Arnoldi method, which projects highdimensional tensor problems onto lower-dimensional tensor Krylov subspaces. The derived method exploits novel algebraic properties of the t-product to address large-scale tensor computations efficiently. Applications include the evaluation of parameter-dependent tensor functions and the solution of multidimensional ordinary differential equations. Numerical experiments illustrate the effectiveness and accuracy of the proposed methods compared with other approaches.
ER -