A Lanczos-type procedure for tensors

Cipolla, Stefano, Pozza, Stefano, Redivo-Zaglia, Michela and Van Buggenhout, Niel (2023) A Lanczos-type procedure for tensors. Numerical Algorithms, 92, 377-406. (doi:10.1007/s11075-022-01351-6).

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Abstract

The solution of linear non-autonomous ordinary differential equation systems (also known as the time-ordered exponential) is a computationally challenging problem arising in a variety of applications. In this work, we present and study a new framework for the computation of bilinear forms involving the time-ordered exponential. Such a framework is based on an extension of the non-Hermitian Lanczos algorithm to 4-mode tensors. Detailed results concerning its theoretical properties are presented. Moreover, computational results performed on real-world problems confirm the effectiveness of our approach.

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Accepted/In Press date: 7 June 2022

e-pub ahead of print date: 31 August 2022

Published date: January 2023

Additional Information: Funding Information: the authors want to thank Enikö Baligács and Christian Bonhomme (Laboratoire de chimie de la matière condensée de Paris, Sorbonne University) for providing the data from real-world applications used in Section . This work was supported by Charles University Research programs No. PRIMUS/21/SCI/009 and UNCE/SCI/023, and by the Magica project ANR-20-CE29-0007 funded by the French National Research Agency. The author M.R.-Z. is a member of the GNCS-INdAM group.

Keywords: Lanczos-type procedures for tensors, Non-Hermitian Lanczos algorithm, Time-ordered exponential, ⋆-Lanczos algorithm