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Volume 18, Issue 3
Variable $s$-Step Technique for New Conjugate Residual Algorithms for Solving Non-Square Linear Systems Arising in Control Problems

Hojjatollah Shokri Kaveh, Masoud Hajarian & Anthony T. Chronopoulos

DOI: 10.4208/nmtma.OA-2024-0109

Numer. Math. Theor. Meth. Appl., 18 (2025), pp. 598-618.

Published online: 2025-09

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  • Abstract

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.

  • Keywords

Non-square linear system, $s$-step algorithm, control system, least square problem, Krylov subspace method.

  • AMS Subject Headings

65F18, 65F10, 65J10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-18-598, author = {Kaveh , Hojjatollah ShokriHajarian , Masoud and Chronopoulos , Anthony T.}, title = {Variable $s$-Step Technique for New Conjugate Residual Algorithms for Solving Non-Square Linear Systems Arising in Control Problems}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2025}, volume = {18}, number = {3}, pages = {598--618}, abstract = {

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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2024-0109}, url = {http://global-sci.org/intro/article_detail/nmtma/24320.html} }
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 -

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.

Kaveh , Hojjatollah ShokriHajarian , Masoud and Chronopoulos , Anthony T.. (2025). Variable $s$-Step Technique for New Conjugate Residual Algorithms for Solving Non-Square Linear Systems Arising in Control Problems. Numerical Mathematics: Theory, Methods and Applications. 18 (3). 598-618. doi:10.4208/nmtma.OA-2024-0109
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