{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,17]],"date-time":"2026-04-17T03:41:49Z","timestamp":1776397309531,"version":"3.51.2"},"reference-count":49,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2025,4,2]],"date-time":"2025-04-02T00:00:00Z","timestamp":1743552000000},"content-version":"vor","delay-in-days":91,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2025,1]]},"abstract":"<jats:p>This work is aimed at deriving a computationally efficient approach to approximate the second\u2010order Index\u20101 descriptor systems without exploiting the fundamental structure of the systems, which ensures both the accuracy of the approximation and the feasibility of computation time. It demonstrates the structure\u2010preserving iterative singular\u2010value decomposition (SVD)\u2010Krylov algorithm (ISKA) which is a hybrid two\u2010sided projections strategy combined with a computationally feasible Krylov subspace technique and the stability\u2010preserving iterative technique based SVD. ISKA is a model\u2010order reduction (MOR) approach utilized to get a reduced\u2010order model (ROM) corresponding to a target model with a desired size, where two projector matrices are the main constituent. The left projector matrix will be constructed using the low\u2010rank Cholesky\u2010factor alternative direction implicit (LRCF\u2010ADI) technique, whereas the right projector matrix will be constructed utilizing the well\u2010known Krylov subspace. The main focus of this work is to avoid the so\u2010called first\u2010order conversion of the second\u2010order systems and ensure the invariance of the matrix\u2010vector operations of the original systems. A real\u2010world model derived from the adaptive spindle support system will be utilized as the target model to numerically validate the competency and efficiency of the proposed strategy through MATLAB simulations. Accuracy of the approximation, stability of the ROMs, and optimization of computational time are the prime concerns of this work. To confirm the advancement of the proposed approach, it will be compared with the existing approaches employing the necessary figures and tables.<\/jats:p>","DOI":"10.1155\/jama\/5976163","type":"journal-article","created":{"date-parts":[[2025,4,4]],"date-time":"2025-04-04T02:56:11Z","timestamp":1743735371000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["SVD\u2010Krylov\u2013Based Structure\u2010Preserving Techniques for Approximation of a Class of Second\u2010Order Index\u20101 Descriptor Systems"],"prefix":"10.1155","volume":"2025","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6526-9276","authenticated-orcid":false,"given":"Mahtab","family":"Uddin","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9817-6156","authenticated-orcid":false,"given":"M. Monir","family":"Uddin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2700-6261","authenticated-orcid":false,"given":"Md. Abdul Hakim","family":"Khan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2025,4,2]]},"reference":[{"key":"e_1_2_10_1_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4419-6397-0"},{"key":"e_1_2_10_2_2","volume-title":"Numerical Study on Continuous-Time Algebraic Riccati Equations Arising from Large-Scale Sparse Descriptor Systems","author":"Uddin M.","year":"2020"},{"key":"e_1_2_10_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-72480-1_1"},{"key":"e_1_2_10_4_2","doi-asserted-by":"publisher","DOI":"10.1109\/MCS.2004.1272745"},{"key":"e_1_2_10_5_2","volume-title":"Issues in Interpolatory Model Reduction: Inexact Solves, Second-Order Systems and Daes","author":"Wyatt S. A.","year":"2012"},{"key":"e_1_2_10_6_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-05083-6_11"},{"key":"e_1_2_10_7_2","doi-asserted-by":"publisher","DOI":"10.1080\/13873950701844170"},{"key":"e_1_2_10_8_2","doi-asserted-by":"publisher","DOI":"10.1186\/s13362-021-00109-4"},{"key":"e_1_2_10_9_2","doi-asserted-by":"publisher","DOI":"10.37256\/cm.5120243646"},{"key":"e_1_2_10_10_2","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898718003"},{"key":"e_1_2_10_11_2","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511615115"},{"key":"e_1_2_10_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.arcontrol.2005.08.002"},{"key":"e_1_2_10_13_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11831-014-9111-2"},{"key":"e_1_2_10_14_2","doi-asserted-by":"publisher","DOI":"10.1137\/18M1220960"},{"key":"e_1_2_10_15_2","doi-asserted-by":"publisher","DOI":"10.1007\/s40435-022-00985-7"},{"key":"e_1_2_10_16_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11831-021-09690-8"},{"key":"e_1_2_10_17_2","doi-asserted-by":"publisher","DOI":"10.1137\/070684562"},{"key":"e_1_2_10_18_2","doi-asserted-by":"publisher","DOI":"10.1002\/gamm.201310003"},{"key":"e_1_2_10_19_2","doi-asserted-by":"publisher","DOI":"10.1137\/130932715"},{"key":"e_1_2_10_20_2","volume-title":"Balanced Truncation Model Reduction for Largescale Systems in Descriptor Form","author":"Mehrmann V.","year":"2005"},{"key":"e_1_2_10_21_2","doi-asserted-by":"publisher","DOI":"10.1137\/070681910"},{"key":"e_1_2_10_22_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11740-012-0410-x"},{"key":"e_1_2_10_23_2","doi-asserted-by":"publisher","DOI":"10.1080\/13873954.2013.794363"},{"key":"e_1_2_10_24_2","doi-asserted-by":"publisher","DOI":"10.1137\/17M1148797"},{"key":"e_1_2_10_25_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2017.10.006"},{"key":"e_1_2_10_26_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.sysconle.2012.03.005"},{"key":"e_1_2_10_27_2","doi-asserted-by":"publisher","DOI":"10.1137\/140998081"},{"key":"e_1_2_10_28_2","volume-title":"Iterative Rational Krylov Algorithm for Unstable Dynamical Systems and Genaralized Coprime Factorizations","author":"Sinani K.","year":"2016"},{"key":"e_1_2_10_29_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11740-020-00995-4"},{"key":"e_1_2_10_30_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.sysconle.2011.04.013"},{"key":"e_1_2_10_31_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.apnum.2011.09.007"},{"key":"e_1_2_10_32_2","doi-asserted-by":"publisher","DOI":"10.1002\/nla.1936"},{"key":"e_1_2_10_33_2","doi-asserted-by":"publisher","DOI":"10.1109\/TPWRS.2008.926693"},{"key":"e_1_2_10_34_2","doi-asserted-by":"publisher","DOI":"10.1137\/070711578"},{"key":"e_1_2_10_35_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2022.01.035"},{"key":"e_1_2_10_36_2","volume-title":"Model Reduction of Large Linear Systems via Low Rank System Gramians","author":"Li J. R.","year":"2000"},{"key":"e_1_2_10_37_2","first-page":"113","article-title":"Two Efficient SVD\/Krylov Algorithms for Model Order Reduction of Large Scale Systems","volume":"38","author":"Chahlaoui Y.","year":"2011","journal-title":"Electronic Transactions On Numerical Analysis (ETNA)"},{"key":"e_1_2_10_38_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2011.07.022"},{"key":"e_1_2_10_39_2","doi-asserted-by":"publisher","DOI":"10.1109\/ISGT.2016.7781027"},{"key":"e_1_2_10_40_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2007.10.041"},{"key":"e_1_2_10_41_2","doi-asserted-by":"publisher","DOI":"10.38032\/jea.2021.03.002"},{"key":"e_1_2_10_42_2","doi-asserted-by":"publisher","DOI":"10.1007\/s40435-023-01159-9"},{"key":"e_1_2_10_43_2","doi-asserted-by":"publisher","DOI":"10.3934\/mmc.2021006"},{"key":"e_1_2_10_44_2","volume-title":"First-Order Representations of Linear Systems","author":"Kuijper M.","year":"2012"},{"key":"e_1_2_10_45_2","doi-asserted-by":"publisher","DOI":"10.1137\/060673977"},{"key":"e_1_2_10_46_2","volume-title":"Structure-Preserving Model Reduction for Mechanical Systems","author":"Werner S. W.","year":"2021"},{"key":"e_1_2_10_47_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-15260-8_15"},{"key":"e_1_2_10_48_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-2789(03)00227-6"},{"key":"e_1_2_10_49_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cirp.2008.03.051"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/jama\/5976163","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1155\/jama\/5976163","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/jama\/5976163","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,17]],"date-time":"2026-04-17T02:44:11Z","timestamp":1776393851000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/jama\/5976163"}},"subtitle":[],"editor":[{"given":"Qing-Wen","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2025,1]]},"references-count":49,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2025,1]]}},"alternative-id":["10.1155\/jama\/5976163"],"URL":"https:\/\/doi.org\/10.1155\/jama\/5976163","archive":["Portico"],"relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"value":"1110-757X","type":"print"},{"value":"1687-0042","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,1]]},"assertion":[{"value":"2024-10-18","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-02-27","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-04-02","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"5976163"}}