{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,10]],"date-time":"2026-07-10T07:16:24Z","timestamp":1783667784708,"version":"3.55.0"},"reference-count":58,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62350410484"],"award-info":[{"award-number":["62350410484"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Journal of Computational and Applied Mathematics"],"published-print":{"date-parts":[[2027,1]]},"DOI":"10.1016\/j.cam.2026.117897","type":"journal-article","created":{"date-parts":[[2026,6,9]],"date-time":"2026-06-09T23:45:59Z","timestamp":1781048759000},"page":"117897","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["A unified low-rank ADI framework with shared linear solves for simultaneously solving multiple Lyapunov, Sylvester, and Riccati equations"],"prefix":"10.1016","volume":"489","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3933-8837","authenticated-orcid":false,"given":"Umair","family":"Zulfiqar","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhong-Yi","family":"Huang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0006-4147-5514","authenticated-orcid":false,"given":"Qiu-Yan","family":"Song","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhi-Yuan","family":"Gao","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"issue":"1","key":"10.1016\/j.cam.2026.117897_bib0001","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1002\/gamm.201310003","article-title":"Numerical solution of large and sparse continuous time algebraic matrix Riccati and Lyapunov equations: a state of the art survey","volume":"36","author":"Benner","year":"2013","journal-title":"GAMM-Mitt."},{"issue":"1","key":"10.1016\/j.cam.2026.117897_bib0002","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/0893-9659(88)90183-8","article-title":"Iterative solution of the Lyapunov matrix equation","volume":"1","author":"Wachspress","year":"1988","journal-title":"Appl. Math. Lett."},{"issue":"2","key":"10.1016\/j.cam.2026.117897_bib0003","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1007\/s11075-012-9569-7","article-title":"Efficient handling of complex shift parameters in the low-rank Cholesky factor ADI method","volume":"62","author":"Benner","year":"2013","journal-title":"Numer. Algorithms"},{"issue":"1","key":"10.1016\/j.cam.2026.117897_bib0004","doi-asserted-by":"crossref","first-page":"585","DOI":"10.1002\/pamm.201310273","article-title":"A reformulated low-rank ADI iteration with explicit residual factors","volume":"13","author":"Benner","year":"2013","journal-title":"PAMM"},{"issue":"4","key":"10.1016\/j.cam.2026.117897_bib0005","doi-asserted-by":"crossref","first-page":"915","DOI":"10.1137\/S0895479897317685","article-title":"An asynchronous parallel supernodal algorithm for sparse Gaussian elimination","volume":"20","author":"Demmel","year":"1999","journal-title":"SIAM J. Matrix Anal. Appl."},{"issue":"3","key":"10.1016\/j.cam.2026.117897_bib0006","doi-asserted-by":"crossref","first-page":"720","DOI":"10.1137\/S0895479895291765","article-title":"A supernodal approach to sparse partial pivoting","volume":"20","author":"Demmel","year":"1999","journal-title":"SIAM J. Matrix Anal. Appl."},{"issue":"2","key":"10.1016\/j.cam.2026.117897_bib0007","doi-asserted-by":"crossref","first-page":"196","DOI":"10.1145\/992200.992206","article-title":"Algorithm 832: UMFPACK v4.3\u2014an unsymmetric-pattern multifrontal method","volume":"30","author":"Davis","year":"2004","journal-title":"ACM Trans. Math. Softw."},{"issue":"1","key":"10.1016\/j.cam.2026.117897_bib0008","doi-asserted-by":"crossref","first-page":"A471","DOI":"10.1137\/15M1030911","article-title":"Frequency-limited balanced truncation with low-rank approximations","volume":"38","author":"Benner","year":"2016","journal-title":"SIAM J. Sci. Comput."},{"issue":"6","key":"10.1016\/j.cam.2026.117897_bib0009","doi-asserted-by":"crossref","first-page":"1821","DOI":"10.1007\/s10444-018-9608-6","article-title":"Balanced truncation model order reduction in limited time intervals for large systems","volume":"44","author":"K\u00fcrschner","year":"2018","journal-title":"Adv. Comput. Math."},{"key":"10.1016\/j.cam.2026.117897_bib0010","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1016\/j.laa.2015.04.006","article-title":"On the benefits of the LDL\u22a4 factorization for large-scale differential matrix equation solvers","volume":"480","author":"Lang","year":"2015","journal-title":"Linear Algebra Appl."},{"issue":"10","key":"10.1016\/j.cam.2026.117897_bib0011","doi-asserted-by":"crossref","first-page":"1687","DOI":"10.1109\/9.467681","article-title":"Frequency-weighted L\u221e norm and optimal Hankel norm model reduction","volume":"40","author":"Zhou","year":"1995","journal-title":"IEEE Trans. Autom. Control"},{"issue":"2","key":"10.1016\/j.cam.2026.117897_bib0012","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1007\/s00211-017-0907-5","article-title":"RADI: a low-rank ADI-type algorithm for large scale algebraic Riccati equations","volume":"138","author":"Benner","year":"2018","journal-title":"Numer. Math."},{"key":"10.1016\/j.cam.2026.117897_bib0013","series-title":"Matrix Computations","author":"Golub","year":"2013"},{"issue":"4","key":"10.1016\/j.cam.2026.117897_bib0014","doi-asserted-by":"crossref","first-page":"1035","DOI":"10.1016\/j.cam.2009.08.108","article-title":"On the ADI method for Sylvester equations","volume":"233","author":"Benner","year":"2009","journal-title":"J. Comput. Appl. Math."},{"issue":"9","key":"10.1016\/j.cam.2026.117897_bib0015","doi-asserted-by":"crossref","first-page":"1656","DOI":"10.1016\/j.camwa.2014.03.004","article-title":"Computing real low-rank solutions of Sylvester equations by the factored ADI method","volume":"67","author":"Benner","year":"2014","journal-title":"Comput. Math. Appl."},{"issue":"256\u2013270","key":"10.1016\/j.cam.2026.117897_bib0016","first-page":"27","article-title":"Cross-gramian based model reduction for data-sparse systems","volume":"31","author":"Baur","year":"2008","journal-title":"Electron. Trans. Numer. Anal."},{"key":"10.1016\/j.cam.2026.117897_bib0017","series-title":"Essentials of Robust Control","volume":"104","author":"Zhou","year":"1998"},{"key":"10.1016\/j.cam.2026.117897_bib0018","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1016\/0024-3795(88)90166-8","article-title":"Balanced stochastic realizations","volume":"98","author":"Green","year":"1988","journal-title":"Linear Algebra Appl."},{"key":"10.1016\/j.cam.2026.117897_bib0019","series-title":"Proceedings of the 39th Annual Design Automation Conference","first-page":"52","article-title":"Guaranteed passive balancing transformations for model order reduction","author":"Phillips","year":"2002"},{"key":"10.1016\/j.cam.2026.117897_bib0020","series-title":"Robust and Optimal Control","author":"Zhou","year":"1996"},{"key":"10.1016\/j.cam.2026.117897_bib0021","series-title":"Model Reduction for Control System Design","author":"Obinata","year":"2012"},{"issue":"2","key":"10.1016\/j.cam.2026.117897_bib0022","doi-asserted-by":"crossref","first-page":"752","DOI":"10.3182\/20120215-3-AT-3016.00133","article-title":"A goal-oriented dual LRCF-ADI for balanced truncation","volume":"45","author":"Saak","year":"2012","journal-title":"IFAC Proc. Vol."},{"key":"10.1016\/j.cam.2026.117897_bib0023","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1016\/j.laa.2024.01.020","article-title":"On a family of low-rank algorithms for large-scale algebraic Riccati equations","volume":"687","author":"Bertram","year":"2024","journal-title":"Linear Algebra Appl."},{"key":"10.1016\/j.cam.2026.117897_bib0024","series-title":"Model Reduction and Approximation: Theory and Algorithms","first-page":"297","article-title":"Chapter 7: model reduction by rational interpolation","author":"Beattie","year":"2017"},{"key":"10.1016\/j.cam.2026.117897_bib0025","series-title":"H2 Pseudo-Optimal Model Order Reduction","author":"Wolf","year":"2014"},{"key":"10.1016\/j.cam.2026.117897_bib0026","series-title":"Model Order Reduction by Krylov Subspace Methods with Global Error Bounds and Automatic Choice of Parameters","author":"Panzer","year":"2014"},{"key":"10.1016\/j.cam.2026.117897_bib0027","series-title":"2013 American Control Conference","first-page":"5512","article-title":"A greedy rational Krylov method for H2-pseudooptimal model order reduction with preservation of stability","author":"Panzer","year":"2013"},{"issue":"3","key":"10.1016\/j.cam.2026.117897_bib0028","doi-asserted-by":"crossref","first-page":"481","DOI":"10.1080\/00207179.2015.1081985","article-title":"The ADI iteration for Lyapunov equations implicitly performs H2 pseudo-optimal model order reduction","volume":"89","author":"Wolf","year":"2016","journal-title":"Int. J. Control"},{"issue":"1","key":"10.1016\/j.cam.2026.117897_bib0029","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1016\/j.cam.2003.08.026","article-title":"Sylvester equations and projection-based model reduction","volume":"162","author":"Gallivan","year":"2004","journal-title":"J. Comput. Appl. Math."},{"issue":"2","key":"10.1016\/j.cam.2026.117897_bib0030","doi-asserted-by":"crossref","first-page":"1083","DOI":"10.1007\/s11075-022-01331-w","article-title":"A low-rank solution method for Riccati equations with indefinite quadratic terms","volume":"92","author":"Benner","year":"2023","journal-title":"Numer. Algorithms"},{"key":"10.1016\/j.cam.2026.117897_bib0031","series-title":"Linear System Theory","author":"Rugh","year":"1996"},{"issue":"1","key":"10.1016\/j.cam.2026.117897_bib0032","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1002\/nla.1936","article-title":"A new subspace iteration method for the algebraic Riccati equation","volume":"22","author":"Lin","year":"2015","journal-title":"Numer. Linear Algebra Appl."},{"key":"10.1016\/j.cam.2026.117897_bib0033","series-title":"Technical Report","article-title":"Sparse-dense Sylvester equations in H2-model order reduction","author":"Benner","year":"2011"},{"key":"10.1016\/j.cam.2026.117897_bib0034","unstructured":"U. Zulfiqar, Data-driven implementations of various generalizations of balanced truncation (2025). arXiv preprint arXiv: 2506.23204."},{"issue":"1","key":"10.1016\/j.cam.2026.117897_bib0035","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1109\/TAC.1981.1102568","article-title":"Principal component analysis in linear systems: controllability, observability, and model reduction","volume":"26","author":"Moore","year":"2003","journal-title":"IEEE Trans. Autom. Control"},{"issue":"10","key":"10.1016\/j.cam.2026.117897_bib0036","doi-asserted-by":"crossref","first-page":"953","DOI":"10.1109\/TAC.1983.1103159","article-title":"A new set of invariants for linear systems\u2013application to reduced order compensator design","volume":"28","author":"Jonckheere","year":"2003","journal-title":"IEEE Trans. Autom. Control"},{"issue":"6","key":"10.1016\/j.cam.2026.117897_bib0037","doi-asserted-by":"crossref","first-page":"668","DOI":"10.1109\/9.86941","article-title":"Controller reduction by H\u221e-balanced truncation","volume":"36","author":"Mustafa","year":"2002","journal-title":"IEEE Trans. Autom. Control"},{"issue":"1","key":"10.1016\/j.cam.2026.117897_bib0038","doi-asserted-by":"crossref","first-page":"743","DOI":"10.1109\/TPWRS.2016.2556747","article-title":"Low computational complexity model reduction of power systems with preservation of physical characteristics","volume":"32","author":"Scarciotti","year":"2016","journal-title":"IEEE Trans. Power Syst."},{"key":"10.1016\/j.cam.2026.117897_bib0039","series-title":"Dynamics and Control of Structures: A Modal Approach","author":"Gawronski","year":"2004"},{"key":"10.1016\/j.cam.2026.117897_bib0040","series-title":"Structure-Preserving Model Reduction for Mechanical Systems","author":"Werner","year":"2021"},{"issue":"3","key":"10.1016\/j.cam.2026.117897_bib0041","doi-asserted-by":"crossref","first-page":"970","DOI":"10.1137\/09074721X","article-title":"A new scaling and squaring algorithm for the matrix exponential","volume":"31","author":"Al-Mohy","year":"2010","journal-title":"SIAM J. Matrix Anal. Appl."},{"issue":"1","key":"10.1016\/j.cam.2026.117897_bib0042","doi-asserted-by":"crossref","first-page":"472","DOI":"10.1137\/17M1129866","article-title":"Multiprecision algorithms for computing the matrix logarithm","volume":"39","author":"Fasi","year":"2018","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"10.1016\/j.cam.2026.117897_bib0043","first-page":"142","article-title":"Self-generating and efficient shift parameters in ADI methods for large Lyapunov and Sylvester equations","volume":"43","author":"Benner","year":"2014","journal-title":"Electron. Trans. Numer. Anal."},{"key":"10.1016\/j.cam.2026.117897_bib0044","series-title":"Numerical Methods for Large Eigenvalue Problems: Revised Edition","author":"Saad","year":"2011"},{"key":"10.1016\/j.cam.2026.117897_bib0045","series-title":"Model Order Reduction: Theory, Research Aspects and Applications","first-page":"177","article-title":"Modal approximation and computation of dominant poles","author":"Rommes","year":"2008"},{"key":"10.1016\/j.cam.2026.117897_bib0046","series-title":"Methods for Eigenvalue Problems with Applications in Model Order Reduction","author":"Rommes","year":"2007"},{"key":"10.1016\/j.cam.2026.117897_bib0047","series-title":"Efficient Numerical Solution of Large Scale Algebraic Matrix Equations in PDE Control and Model Order Reduction","author":"Saak","year":"2009"},{"issue":"4","key":"10.1016\/j.cam.2026.117897_bib0048","doi-asserted-by":"crossref","first-page":"A2412","DOI":"10.1137\/21M1434349","article-title":"Large-scale estimation of dominant poles of a transfer function by an interpolatory framework","volume":"44","author":"Mengi","year":"2022","journal-title":"SIAM J. Sci. Comput."},{"issue":"1","key":"10.1016\/j.cam.2026.117897_bib0049","doi-asserted-by":"crossref","first-page":"162","DOI":"10.1109\/59.486093","article-title":"Computing dominant poles of power system transfer functions","volume":"11","author":"Martins","year":"1996","journal-title":"IEEE Trans. Power Syst."},{"key":"10.1016\/j.cam.2026.117897_bib0050","series-title":"Preprint","article-title":"A Galerkin-Newton-ADI Method for Solving Large-Scale Algebraic Riccati Equations","author":"Benner","year":"2010"},{"issue":"4","key":"10.1016\/j.cam.2026.117897_bib0051","doi-asserted-by":"crossref","first-page":"1471","DOI":"10.1109\/TPWRS.2006.881154","article-title":"Efficient computation of multivariable transfer function dominant poles using subspace acceleration","volume":"21","author":"Rommes","year":"2006","journal-title":"IEEE Trans. Power Syst."},{"key":"10.1016\/j.cam.2026.117897_bib0052","unstructured":"U. Zulfiqar, Z.-H. Xiao, Q. y. Song, V. Sreeram, Balanced truncation via tangential interpolation, 2024, arXiv preprint arXiv: 2409.13358."},{"key":"10.1016\/j.cam.2026.117897_bib0053","unstructured":"U. Zulfiqar, MATLAB codes for \u201cA unified low-rank ADI framework with shared linear solves for simultaneously solving multiple Lyapunov, Sylvester, and Riccati equations\u201d, 2024, 10.5281\/zenodo.17802009."},{"key":"10.1016\/j.cam.2026.117897_bib0054","series-title":"Model Reduction of Complex Dynamical Systems","first-page":"369","article-title":"Matrix Equations, Sparse Solvers: M-MESS-2.0. 1-Philosophy, Features, and Application for (Parametric) Model Order Reduction","author":"Benner","year":"2021"},{"issue":"2\u20133","key":"10.1016\/j.cam.2026.117897_bib0055","doi-asserted-by":"crossref","first-page":"322","DOI":"10.1016\/j.laa.2006.01.007","article-title":"Algorithms for model reduction of large dynamical systems","volume":"415","author":"Penzl","year":"2006","journal-title":"Linear Algebra Appl."},{"key":"10.1016\/j.cam.2026.117897_bib0056","series-title":"Applied and Computational Control, Signals, and Circuits","first-page":"499","article-title":"SLICOT-A subroutine library in systems and control theory","volume":"1","author":"Benner","year":"1999"},{"key":"10.1016\/j.cam.2026.117897_bib0057","series-title":"Dimension Reduction of Large-Scale Systems: Proceedings of a Workshop Held in Oberwolfach, Germany, October 19\u201325, 2003","first-page":"379","article-title":"Benchmark examples for model reduction of linear time-invariant dynamical systems","author":"Chahlaoui","year":"2005"},{"key":"10.1016\/j.cam.2026.117897_bib0058","series-title":"Dimension Reduction of Large-Scale Systems: Proceedings of a Workshop Held in Oberwolfach, Germany, October 19\u201325, 2003","first-page":"353","article-title":"A semi-discretized heat transfer model for optimal cooling of steel profiles","author":"Benner","year":"2005"}],"container-title":["Journal of Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S037704272600539X?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S037704272600539X?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,7,10]],"date-time":"2026-07-10T06:46:31Z","timestamp":1783665991000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S037704272600539X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2027,1]]},"references-count":58,"alternative-id":["S037704272600539X"],"URL":"https:\/\/doi.org\/10.1016\/j.cam.2026.117897","relation":{},"ISSN":["0377-0427"],"issn-type":[{"value":"0377-0427","type":"print"}],"subject":[],"published":{"date-parts":[[2027,1]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"A unified low-rank ADI framework with shared linear solves for simultaneously solving multiple Lyapunov, Sylvester, and Riccati equations","name":"articletitle","label":"Article Title"},{"value":"Journal of Computational and Applied Mathematics","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.cam.2026.117897","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"117897"}}