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arXiv · 2609.11369

The tubal Arnoldi method for tensor function approximation

Fatima Bouyghf·Mohamed El Ghomari·Alaa El Ichi
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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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Fatima Bouyghf, Mohamed El Ghomari, Alaa El Ichi. 2026-09-10. The tubal Arnoldi method for tensor function approximation. https://arxiv.org/abs/2609.11369

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