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A Lanczos-type procedure for tensors

Publication at Faculty of Mathematics and Physics |
2023

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.