TY - JOUR
T1 - Variable $s$-Step Technique for New Conjugate Residual Algorithms for Solving Non-Square Linear Systems Arising in Control Problems
AU - Kaveh , Hojjatollah Shokri
AU - Hajarian , Masoud
AU - Chronopoulos , Anthony T.
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 3
SP - 598
EP - 618
PY - 2025
DA - 2025/09
SN - 18
DO - http://doi.org/10.4208/nmtma.OA-2024-0109
UR - https://global-sci.org/intro/article_detail/nmtma/24320.html
KW - Non-square linear system, $s$-step algorithm, control system, least square problem, Krylov subspace method.
AB - <p style="text-align: justify;">This paper introduces two algorithms based on the conjugate residual
method and variable $s$-step for solving linear systems with non-square coefficient
matrices. The introduced algorithms demonstrate their effectiveness through numerical comparisons with other methods, specifically CGNE and CGNR, to solve
non-square linear systems. The approach aims to enhance the efficiency of solving
problems related to control systems and imaging underground layers, particularly in
the context of seismic tomography.</p>