A Lanczos-type procedure for tensors

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 variety applications. In this work, we present and study new framework for computation bilinear forms involving exponential. Such based on an extension non-Hermitian Lanczos algorithm to 4-mode tensors. Detailed results concerning its theoretical properties are presented. Moreover, computational performed real-world problems confirm effectiveness our approach.