{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,26]],"date-time":"2025-07-26T08:55:47Z","timestamp":1753520147175},"reference-count":24,"publisher":"Springer Science and Business Media LLC","issue":"8","license":[{"start":{"date-parts":[[2021,10,12]],"date-time":"2021-10-12T00:00:00Z","timestamp":1633996800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,10,12]],"date-time":"2021-10-12T00:00:00Z","timestamp":1633996800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comp. Appl. Math."],"published-print":{"date-parts":[[2021,12]]},"DOI":"10.1007\/s40314-021-01654-9","type":"journal-article","created":{"date-parts":[[2021,10,13]],"date-time":"2021-10-13T00:57:21Z","timestamp":1634086641000},"update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["An DRCS preconditioning iterative method for a constrained fractional optimal control problem"],"prefix":"10.1007","volume":"40","author":[{"given":"Shi-Ping","family":"Tang","sequence":"first","affiliation":[]},{"given":"Yu-Mei","family":"Huang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,10,12]]},"reference":[{"key":"1654_CR1","doi-asserted-by":"publisher","first-page":"323","DOI":"10.1007\/s11071-004-3764-6","volume":"38","author":"O Agrawal","year":"2004","unstructured":"Agrawal O (2004) A general formulation and solution scheme for fractional optimal control problems. Nonlinear Dyn 38:323\u2013337","journal-title":"Nonlinear Dyn"},{"issue":"2","key":"1654_CR2","doi-asserted-by":"publisher","first-page":"323","DOI":"10.1007\/s11071-004-3764-6","volume":"38","author":"OP Agrawal","year":"2004","unstructured":"Agrawal OP (2004) A general formulation and solution scheme for fractional optimal control problems. Nonlinear Dyn 38(2):323\u2013337","journal-title":"Nonlinear Dyn"},{"key":"1654_CR3","doi-asserted-by":"publisher","first-page":"126","DOI":"10.1016\/j.apnum.2021.01.011","volume":"163","author":"ZZ Bai","year":"2021","unstructured":"Bai ZZ, Lu KY (2021) Optimal rotated block-diagonal preconditioning for discretized optimal control problems constrained with fractional time-dependent diffusive equations. Appl Numer Math 163:126\u2013146","journal-title":"Appl Numer Math"},{"issue":"4","key":"1654_CR4","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1002\/nla.2093","volume":"24","author":"ZZ Bai","year":"2017","unstructured":"Bai ZZ, Lu KY, Pan JY (2017) Diagonal and Toeplitz splitting iteration methods for diagonal-plus-Toeplitz linear systems from spatial fractional diffusion equations. Numer Linear Algebra Appl 24(4):1\u201315","journal-title":"Numer Linear Algebra Appl"},{"key":"1654_CR5","doi-asserted-by":"crossref","unstructured":"Chan RH, Jin XQ (2007) An introduction to iterative Toeplitz solvers. Society for Industrial and Applied Mathematics, Philadelphia","DOI":"10.1137\/1.9780898718850"},{"issue":"4","key":"1654_CR6","doi-asserted-by":"publisher","first-page":"542","DOI":"10.1137\/0610039","volume":"10","author":"RH Chan","year":"1989","unstructured":"Chan RH (1989) Circulant preconditioners for Hermitian Toeplitz systems. SIAM J Matrix Anal Appl 10(4):542\u2013550","journal-title":"SIAM J Matrix Anal Appl"},{"issue":"3","key":"1654_CR7","doi-asserted-by":"publisher","first-page":"1472","DOI":"10.1016\/j.camwa.2011.03.025","volume":"62","author":"R Dorville","year":"2011","unstructured":"Dorville R, Mophou GM, Valmorin VS (2011) Optimal control of a nonhomogeneous Dirichlet boundary fractional diffusion equation. Comput Math Appl 62(3):1472\u20131481","journal-title":"Comput Math Appl"},{"issue":"2","key":"1654_CR8","doi-asserted-by":"publisher","first-page":"259","DOI":"10.4208\/jcm.1612-m2016-0696","volume":"36","author":"N Du","year":"2018","unstructured":"Du N, Shen WF (2018) A fast stochastic Galerkin method for a constrained optimal control problem governed by a random fractional diffusion equation. J Comput Math 36(2):259\u2013275","journal-title":"J Comput Math"},{"issue":"1","key":"1654_CR9","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10915-015-0125-1","volume":"68","author":"N Du","year":"2016","unstructured":"Du N, Wang H, Liu WB (2016) A fast gradient projection method for a constrained fractional optimal control. J Sci Comput 68(1):1\u201320","journal-title":"J Sci Comput"},{"key":"1654_CR10","first-page":"479","volume":"3","author":"G Frederico","year":"2008","unstructured":"Frederico G, Torres D (2008) Fractional optimal control in the sense of caputo and the fractional Noethers theorem. Int Math Forum 3:479\u2013493","journal-title":"Int Math Forum"},{"key":"1654_CR11","unstructured":"Frederico G, Torres D (2008) Fractional optimal control in the sense of Caputo and the fractional Noether\u2019s theorem. Int Math Forum 3(2):479\u2013493"},{"key":"1654_CR12","volume-title":"Matrix computations","author":"GH Golub","year":"2009","unstructured":"Golub GH, Loan CF (2009) Matrix computations, 4th edn. Johns Hopkins University Press, New York","edition":"4"},{"issue":"1","key":"1654_CR13","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1007\/s10665-013-9676-z","volume":"93","author":"YM Huang","year":"2015","unstructured":"Huang YM (2015) On $$m$$-step Hermitian and skew-Hermitian splitting preconditioning methods. J Eng Math 93(1):77\u201386","journal-title":"J Eng Math"},{"key":"1654_CR14","doi-asserted-by":"publisher","first-page":"3997","DOI":"10.1137\/090753905","volume":"48","author":"K Ito","year":"2010","unstructured":"Ito K, Kunisch K (2010) Semismooth Newton methods for time-optimal control for a class of ODEs. SIAM J Control Optim 48:3997\u20134013","journal-title":"SIAM J Control Optim"},{"key":"1654_CR15","doi-asserted-by":"publisher","first-page":"2083","DOI":"10.1137\/100784667","volume":"49","author":"K Ito","year":"2011","unstructured":"Ito K, Kunisch K (2011) Minimal effort problems and their treatment by semi smooth Newton methods. SIAM J Control Optim 49:2083\u20132100","journal-title":"SIAM J Control Optim"},{"key":"1654_CR16","volume-title":"Adaptive finite element methods for optimal control governed by PDEs","author":"WB Liu","year":"2008","unstructured":"Liu WB, Yan NN (2008) Adaptive finite element methods for optimal control governed by PDEs. Science Press, Beijing"},{"key":"1654_CR17","doi-asserted-by":"publisher","first-page":"589","DOI":"10.4208\/jcm.1103-m3514","volume":"29","author":"HF Niu","year":"2011","unstructured":"Niu HF, Yang DP (2011) Finite element analysis of optimal control problem governed by Stokes equations with $$L^{2}$$-norm state-constraints. J Comput Math 29:589\u2013604","journal-title":"J Comput Math"},{"key":"1654_CR18","doi-asserted-by":"publisher","first-page":"562","DOI":"10.4208\/nmtma.2011.m1101","volume":"4","author":"H Roos","year":"2011","unstructured":"Roos H, Reibiger C (2011) Numerical analysis of a system of singularly perturbed convection-diffusion equations related to optimal control. Numer Math Theory Methods Appl 4:562\u2013575","journal-title":"Numer Math Theory Methods Appl"},{"key":"1654_CR19","doi-asserted-by":"crossref","unstructured":"Saad Y (2003) Iterative methods for sparse linear systems. Society for Industrial and Applied Mathematics, Philadelphia","DOI":"10.1137\/1.9780898718003"},{"issue":"294","key":"1654_CR20","doi-asserted-by":"publisher","first-page":"1703","DOI":"10.1090\/S0025-5718-2015-02917-2","volume":"84","author":"WY Tian","year":"2015","unstructured":"Tian WY, Zhou H, Deng WH (2015) A class of second order difference approximations for solving space fractional diffusion equations. Math Comput 84(294):1703\u20131727","journal-title":"Math Comput"},{"key":"1654_CR21","doi-asserted-by":"publisher","first-page":"99","DOI":"10.4208\/nmtma.2011.m12si06","volume":"5","author":"M Vallejos","year":"2012","unstructured":"Vallejos M (2012) Multigrid methods for elliptic optimal control problems with pointwise state constraints. Numer Math Theory Methods Appl 5:99\u2013109","journal-title":"Numer Math Theory Methods Appl"},{"key":"1654_CR22","doi-asserted-by":"crossref","unstructured":"Wathen AJ (2015) Preconditioning. Acta Numer","DOI":"10.1017\/S0962492915000021"},{"key":"1654_CR23","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1155\/2018\/8697647","volume":"2018","author":"DT Zeng","year":"2018","unstructured":"Zeng DT, Yu X, Huang JF, Tan CQ (2018) Numerical computation for a kind of time optimal control problem for the tubular reactor system. Math Problems Eng 2018:1\u20139","journal-title":"Math Problems Eng"},{"key":"1654_CR24","doi-asserted-by":"publisher","first-page":"174","DOI":"10.1016\/j.apnum.2019.08.024","volume":"147","author":"ZY Zhang","year":"2020","unstructured":"Zhang ZY, Liang D, Wang QS (2020) Immersed finite element method and its analysis for parabolic optimal control problems with interfaces. Appl Numer Math 147:174\u2013195","journal-title":"Appl Numer Math"}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-021-01654-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40314-021-01654-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-021-01654-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,12,3]],"date-time":"2021-12-03T13:13:04Z","timestamp":1638537184000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40314-021-01654-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,10,12]]},"references-count":24,"journal-issue":{"issue":"8","published-print":{"date-parts":[[2021,12]]}},"alternative-id":["1654"],"URL":"https:\/\/doi.org\/10.1007\/s40314-021-01654-9","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"value":"2238-3603","type":"print"},{"value":"1807-0302","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,10,12]]},"assertion":[{"value":"29 June 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 September 2021","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 September 2021","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 October 2021","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"266"}}