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 re...

The form and application of the Lanczos potential for Bianchi spacetime are studied. is found in some specific cases, then general case It leads to two coupled first order partial differential equations which, although they so far have not been solved general, can be many configurations. cosmic energetics: other words study energy gravitational fields Universe.

The Lanczos eigensolution takes the dominant amount of time in most normal modes and modal frequency response analyses. This paper introduces a way to reduce the elapsed time of large eigenvalue jobs by using a newly developed parallel option within the Lanczos algorithm. We will compare the performance of the frequency domain decomposition based distributed memory parallel method introduced in...