Revealing matrices of linear differential systems of arbitrary order
- Authors: Abramov S.A.1, Ryabenko A.A.1, Khmelnov D.E.1
-
Affiliations:
- Dorodnicyn Computing Center
- Issue: Vol 43, No 2 (2017)
- Pages: 67-74
- Section: Article
- URL: https://journals.rcsi.science/0361-7688/article/view/176484
- DOI: https://doi.org/10.1134/S0361768817020025
- ID: 176484
Cite item
Abstract
If the leading matrix of a linear differential system is nonsingular, then its determinant is known to bear useful information about solutions of the system. Of interest is also the frontal matrix. However, each of these matrices (we call them revealing matrices) may occur singular. In the paper, a brief survey of algorithms for transforming a system of full rank to a system with a nonsingular revealing matrix of a desired type is given. The same transformations can be used to check whether the rank of the original system is full. A Maple implementation of these algorithms (package EGRR) is discussed, and results of comparison of estimates of their complexity with actual operation times on a number of examples are presented.
About the authors
S. A. Abramov
Dorodnicyn Computing Center
Author for correspondence.
Email: sergeyabramov@mail.ru
Russian Federation, ul. Vavilova 40, Moscow, 119333
A. A. Ryabenko
Dorodnicyn Computing Center
Email: sergeyabramov@mail.ru
Russian Federation, ul. Vavilova 40, Moscow, 119333
D. E. Khmelnov
Dorodnicyn Computing Center
Email: sergeyabramov@mail.ru
Russian Federation, ul. Vavilova 40, Moscow, 119333