{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,1]],"date-time":"2025-06-01T04:14:56Z","timestamp":1748751296366,"version":"3.41.0"},"reference-count":59,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2016,1,6]],"date-time":"2016-01-06T00:00:00Z","timestamp":1452038400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2016,1,6]],"date-time":"2016-01-06T00:00:00Z","timestamp":1452038400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/100000006","name":"Office of Naval Research","doi-asserted-by":"publisher","award":["N00014-11-1-0068"],"award-info":[{"award-number":["N00014-11-1-0068"]}],"id":[{"id":"10.13039\/100000006","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000006","name":"Office of Naval Research","doi-asserted-by":"publisher","award":["N00014-15-1-2048"],"award-info":[{"award-number":["N00014-15-1-2048"]}],"id":[{"id":"10.13039\/100000006","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["CBET-1404767"],"award-info":[{"award-number":["CBET-1404767"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-1522629"],"award-info":[{"award-number":["DMS-1522629"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"name":"SPAWAR Systems Center Atlantic, Space and Naval Warfare Systems Command","award":["N65236-13-1-1000"],"award-info":[{"award-number":["N65236-13-1-1000"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comput Optim Appl"],"published-print":{"date-parts":[[2016,7]]},"DOI":"10.1007\/s10589-015-9821-x","type":"journal-article","created":{"date-parts":[[2016,1,6]],"date-time":"2016-01-06T15:33:15Z","timestamp":1452094395000},"page":"793-819","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["State-defect constraint pairing graph coarsening method for Karush\u2013Kuhn\u2013Tucker matrices arising in orthogonal collocation methods for optimal control"],"prefix":"10.1007","volume":"64","author":[{"given":"Beg\u00fcm \u015eenses","family":"Cannataro","sequence":"first","affiliation":[]},{"given":"Anil V.","family":"Rao","sequence":"additional","affiliation":[]},{"given":"Timothy A.","family":"Davis","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2016,1,6]]},"reference":[{"issue":"4","key":"9821_CR1","doi-asserted-by":"publisher","first-page":"979","DOI":"10.1137\/S1052623499350013","volume":"12","author":"PE Gill","year":"2002","unstructured":"Gill, P.E., Murray, W., Saunders, M.A.: SNOPT: an SQP algorithm for large-scale constrained optimization. SIAM J. Optim. 12(4), 979\u20131006 (2002)","journal-title":"SIAM J. Optim."},{"issue":"3","key":"9821_CR2","doi-asserted-by":"publisher","first-page":"575","DOI":"10.1016\/j.compchemeng.2008.08.006","volume":"33","author":"LT Biegler","year":"2009","unstructured":"Biegler, L.T., Zavala, V.M.: Large-scale nonlinear programming using IPOPT: an integrating framework for enterprise-wide dynamic optimization. Comput. Chem. Eng. 33(3), 575\u2013582 (2009)","journal-title":"Comput. Chem. Eng."},{"key":"9821_CR3","unstructured":"Duff, I.S., Reid, J.K.: MA47, A Fortran Code for Direct Solution of Indefinite Sparse Symmetric Linear Systems. Report RAL, pp. 95\u2013001 (1995)"},{"issue":"2","key":"9821_CR4","doi-asserted-by":"publisher","first-page":"118","DOI":"10.1145\/992200.992202","volume":"30","author":"IS Duff","year":"2004","unstructured":"Duff, I.S.: MA57\u2014a code for the solution of sparse symmetric definite and indefinite systems. ACM Trans. Math. Softw. 30(2), 118\u2013144 (2004)","journal-title":"ACM Trans. Math. Softw."},{"key":"9821_CR5","volume-title":"MUMPS: A General Purpose Distributed Memory Sparse Solver","author":"PR Amestoy","year":"2001","unstructured":"Amestoy, P.R., Duff, I.S., L\u2019Excellent, J.-Y., Koster, J.: MUMPS: A General Purpose Distributed Memory Sparse Solver. Springer, Heidelberg (2001)"},{"issue":"2","key":"9821_CR6","doi-asserted-by":"publisher","first-page":"187","DOI":"10.1016\/S0167-8191(01)00135-1","volume":"28","author":"O Schenk","year":"2002","unstructured":"Schenk, O., G\u00e4rtner, K.: Two-level dynamic scheduling in PARDISO: improved scalability on shared memory multiprocessing systems. Parallel Comput. 28(2), 187\u2013197 (2002)","journal-title":"Parallel Comput."},{"issue":"10","key":"9821_CR7","doi-asserted-by":"publisher","first-page":"1793","DOI":"10.1109\/9.467672","volume":"40","author":"G Elnagar","year":"1995","unstructured":"Elnagar, G., Kazemi, M., Razzaghi, M.: The pseudospectral legendre method for discretizing optimal control problems. IEEE Trans. Autom. Control 40(10), 1793\u20131796 (1995)","journal-title":"IEEE Trans. Autom. Control"},{"issue":"3","key":"9821_CR8","doi-asserted-by":"publisher","first-page":"227","DOI":"10.1002\/(SICI)1099-1514(199705\/06)18:3<227::AID-OCA598>3.0.CO;2-A","volume":"18","author":"G Elnagar","year":"1998","unstructured":"Elnagar, G., Razzaghi, M.: A collocation-type method for linear quadratic optimal control problems. Optim. Control Appl. Methods 18(3), 227\u2013235 (1998)","journal-title":"Optim. Control Appl. Methods"},{"issue":"2","key":"9821_CR9","doi-asserted-by":"publisher","first-page":"270","DOI":"10.2514\/2.4709","volume":"24","author":"F Fahroo","year":"2001","unstructured":"Fahroo, F., Ross, I.M.: Costate estimation by a legendre pseudospectral method. J. Guidance Control Dyn. 24(2), 270\u2013277 (2001)","journal-title":"J. Guidance Control Dyn."},{"issue":"1","key":"9821_CR10","doi-asserted-by":"publisher","first-page":"160","DOI":"10.2514\/2.4862","volume":"25","author":"F Fahroo","year":"2002","unstructured":"Fahroo, F., Ross, I.M.: Direct trajectory optimization by a Chebyshev pseudospectral method. J. Guidance Control Dyn. 25(1), 160\u2013166 (2002)","journal-title":"J. Guidance Control Dyn."},{"issue":"6","key":"9821_CR11","doi-asserted-by":"publisher","first-page":"1435","DOI":"10.2514\/1.20478","volume":"29","author":"DA Benson","year":"2006","unstructured":"Benson, D.A., Huntington, G.T., Thorvaldsen, T.P., Rao, A.V.: Direct trajectory optimization and costate estimation via an orthogonal collocation method. J Guidance Control Dyn. 29(6), 1435\u20131440 (2006)","journal-title":"J Guidance Control Dyn."},{"issue":"2","key":"9821_CR12","doi-asserted-by":"publisher","first-page":"141","DOI":"10.1007\/BF03256518","volume":"55","author":"GT Huntington","year":"2007","unstructured":"Huntington, G.T., Benson, D.A., Rao, A.V.: Optimal configuration of tetrahedral spacecraft formations. J. Astronaut. Sci. 55(2), 141\u2013169 (2007)","journal-title":"J. Astronaut. Sci."},{"issue":"3","key":"9821_CR13","doi-asserted-by":"publisher","first-page":"689","DOI":"10.2514\/1.31083","volume":"31","author":"GT Huntington","year":"2008","unstructured":"Huntington, G.T., Rao, A.V.: Optimal reconfiguration of spacecraft formations using the Gauss pseudospectral method. J Guidance Control Dyn. 31(3), 689\u2013698 (2008)","journal-title":"J Guidance Control Dyn."},{"key":"9821_CR14","doi-asserted-by":"crossref","unstructured":"Gong, Q., Fahroo, F., Ross, I.M.: Spectral algorithm for pseudospectral methods in optimal control. J Guidance Control Dyn. 31(3), May\u2013June (2008)","DOI":"10.2514\/1.32908"},{"issue":"3","key":"9821_CR15","doi-asserted-by":"publisher","first-page":"307","DOI":"10.1007\/s10589-007-9102-4","volume":"41","author":"Q Gong","year":"2008","unstructured":"Gong, Q., Ross, I.M., Kang, W., Fahroo, F.: Connections between the covector mapping theorem and convergence of pseudospectral methods. Comput. Optim. Appl. 41(3), 307\u2013335 (2008)","journal-title":"Comput. Optim. Appl."},{"key":"9821_CR16","doi-asserted-by":"crossref","unstructured":"Rao, A.V., Benson, D.A., Darby, C.L., Francolin, C., Patterson, M.A., Sanders, I., Huntington, G.T.: Algorithm 902: GPOPS, a matlab software for solving multiple-phase optimal control problems using the Gauss pseudospectral method. ACM Trans. Math. Softw. 37(2), Article 22, 39 pp., April\u2013June (2010)","DOI":"10.1145\/1731022.1731032"},{"issue":"4","key":"9821_CR17","doi-asserted-by":"publisher","first-page":"476","DOI":"10.1002\/oca.957","volume":"32","author":"CL Darby","year":"2011","unstructured":"Darby, C.L., Hager, W.W., Rao, A.V.: An $$hp$$-adaptive pseudospectral method for solving optimal control problems. Optim. Control Appl. Methods 32(4), 476\u2013502 (2011)","journal-title":"Optim. Control Appl. Methods"},{"issue":"3","key":"9821_CR18","doi-asserted-by":"publisher","first-page":"433","DOI":"10.2514\/1.52136","volume":"48","author":"CL Darby","year":"2011","unstructured":"Darby, C.L., Hager, W.W., Rao, A.V.: Direct trajectory optimization using a variable low-order adaptive pseudospectral method. J. Spacecr. Rockets 48(3), 433\u2013445 (2011)","journal-title":"J. Spacecr. Rockets"},{"issue":"1","key":"9821_CR19","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1007\/s10589-007-9098-9","volume":"41","author":"S Kameswaran","year":"2008","unstructured":"Kameswaran, S., Biegler, L.T.: Convergence rates for direct transcription of optimal control problems using collocation at radau points. Comput. Optim. Appl. 41(1), 81\u2013126 (2008)","journal-title":"Comput. Optim. Appl."},{"issue":"2","key":"9821_CR20","doi-asserted-by":"publisher","first-page":"335","DOI":"10.1007\/s10589-009-9291-0","volume":"49","author":"D Garg","year":"2011","unstructured":"Garg, D., Patterson, M.A., Darby, C.L., Francolin, C., Huntington, G.T., Hager, W.W., Rao, A.V.: Direct trajectory optimization and costate estimation of finite-horizon and infinite-horizon optimal control problems via a radau pseudospectral method. Comput. Optim. Appl. 49(2), 335\u2013358 (2011). doi: 10.1007\/s10589-00-09291-0","journal-title":"Comput. Optim. Appl."},{"issue":"11","key":"9821_CR21","doi-asserted-by":"publisher","first-page":"1843","DOI":"10.1016\/j.automatica.2010.06.048","volume":"46","author":"D Garg","year":"2010","unstructured":"Garg, D., Patterson, M.A., Hager, W.W., Rao, A.V., Benson, D.A., Huntington, G.T.: A unified framework for the numerical solution of optimal control problems using pseudospectral methods. Automatica 46(11), 1843\u20131851 (2010). doi: 10.1016\/j.automatica.2010.06.048","journal-title":"Automatica"},{"issue":"4","key":"9821_CR22","doi-asserted-by":"publisher","first-page":"829","DOI":"10.1016\/j.automatica.2011.01.085","volume":"47","author":"D Garg","year":"2011","unstructured":"Garg, D., Hager, W.W., Rao, A.V.: Pseudospectral methods for solving infinite-horizon optimal control problems. Automatica 47(4), 829\u2013837 (2011). doi: 10.1016\/j.automatica.2011.01.085","journal-title":"Automatica"},{"issue":"1","key":"9821_CR23","doi-asserted-by":"publisher","first-page":"1:1","DOI":"10.1145\/2558904","volume":"41","author":"MA Patterson","year":"2014","unstructured":"Patterson, M.A., Rao, A.V.: GPOPS- II: A MATLAB software for solving multiple-phase optimal control problems using hp-adaptive Gaussian quadrature collocation methods and sparse nonlinear programming. ACM Trans. Math. Softw. 41(1), 1:1\u20131:37 (2014)","journal-title":"ACM Trans. Math. Softw."},{"key":"9821_CR24","doi-asserted-by":"publisher","unstructured":"Patterson, M.A., Hager, W.W., Rao, A.V.: A $$ph$$ mesh refinement method for optimal control. Optim. Control Appl. Methods 36(4), 398\u2013421 (2015). doi: 10.1002\/oca2114","DOI":"10.1002\/oca2114"},{"key":"9821_CR25","doi-asserted-by":"publisher","unstructured":"Francolin, C.C., Hager, W.W., Rao, A.V.: Costate approximation in optimal control using integral Gaussian quadrature collocation methods. Optim. Control Appl. Methods 36(4), 381\u2013397 (2015). doi: 10.1002\/oca2112","DOI":"10.1002\/oca2112"},{"issue":"1","key":"9821_CR26","doi-asserted-by":"publisher","first-page":"359","DOI":"10.1137\/S1064827595287997","volume":"20","author":"G Karypis","year":"1998","unstructured":"Karypis, G., Kumar, V.: A fast and high quality multilevel scheme for partitioning irregular graphs. SIAM J. Sci. Comput. 20(1), 359\u2013392 (1998)","journal-title":"SIAM J. Sci. Comput."},{"key":"9821_CR27","doi-asserted-by":"crossref","unstructured":"Pothen, A., Simon, H.D., Wang, L., Barnard, S.T.: Towards a fast implementation of spectral nested dissection. In: Proceedings of the 1992 ACM\/IEEE Conference on Supercomputing, pp. 42\u201351. IEEE Computer Society Press (1992)","DOI":"10.1109\/SUPERC.1992.236711"},{"issue":"3","key":"9821_CR28","doi-asserted-by":"publisher","first-page":"430","DOI":"10.1137\/0611030","volume":"11","author":"A Pothen","year":"1990","unstructured":"Pothen, A., Simon, H.D., Liou, K.-P.: Partitioning sparse matrices with eigenvectors of graphs. SIAM J. Matrix Anal. Appl. 11(3), 430\u2013452 (1990)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"9821_CR29","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-8369-7_3","volume-title":"Automatic Mesh Partitioning","author":"GL Miller","year":"1993","unstructured":"Miller, G.L., Teng, S.-H., Thurston, W., Vavasis, S.A.: Automatic Mesh Partitioning. Springer, Berlin (1993)"},{"key":"9821_CR30","doi-asserted-by":"crossref","unstructured":"Miller, G.L., Teng, S.-H., Vavasis, S.A.: A unified geometric approach to graph separators. In: Proceedings., 32nd Annual Symposium on Foundations of Computer Science, pp. 538\u2013547. IEEE (1991)","DOI":"10.1109\/SFCS.1991.185417"},{"issue":"12","key":"9821_CR31","doi-asserted-by":"publisher","first-page":"1502","DOI":"10.1109\/43.103500","volume":"10","author":"C-K Cheng","year":"1991","unstructured":"Cheng, C.-K., Wei, Y.-C.: An improved two-way partitioning algorithm with stable performance [VLSI]. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 10(12), 1502\u20131511 (1991)","journal-title":"IEEE Trans. Comput. Aided Des. Integr. Circuits Syst."},{"key":"9821_CR32","doi-asserted-by":"crossref","unstructured":"Hendrickson, B., Leland, R.W.: A Multi-level algorithm for partitioning graphs. SC 95, 28 (1995)","DOI":"10.1145\/224170.224228"},{"key":"9821_CR33","doi-asserted-by":"crossref","unstructured":"Mansour, N., Ponnusamy, R., Choudhary, A., Fox, G.: Graph contraction for physical optimization methods: a quality-cost tradeoff for mapping data on parallel computers. In: Proceedings of the 7th International Conference on Supercomputing, pp. 1\u201310. ACM (1993)","DOI":"10.1145\/165939.165942"},{"key":"9821_CR34","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-3748-6","volume-title":"Multilevel Optimization in VLSICAD","author":"J Cong","year":"2003","unstructured":"Cong, J., Shinnerl, J.R.: Multilevel Optimization in VLSICAD. Springer, Berlin (2003)"},{"key":"9821_CR35","volume-title":"Advanced Coarsening Schemes for Graph Partitioning, Experimental Algorithms","author":"I Safro","year":"2012","unstructured":"Safro, I., Sanders, P., Schulz, C.: Advanced Coarsening Schemes for Graph Partitioning, Experimental Algorithms. Springer, Berlin (2012)"},{"key":"9821_CR36","doi-asserted-by":"publisher","first-page":"667","DOI":"10.1007\/s10589-014-9651-2","volume":"59","author":"DP Word","year":"2014","unstructured":"Word, D.P., Kang, J., Akesson, J., Laird, C.D.: Efficient parallel solution of large-scale nonlinear dynamic optimization problems. Comput. Optim. Appl. 59, 667\u2013688 (2014)","journal-title":"Comput. Optim. Appl."},{"issue":"2","key":"9821_CR37","doi-asserted-by":"publisher","first-page":"364","DOI":"10.2514\/1.A32071","volume":"49","author":"MA Patterson","year":"2012","unstructured":"Patterson, M.A., Rao, A.V.: Exploiting sparsity in direct collocation pseudospectral methods for solving optimal control problems. J. Spacecr. Rocket. 49(2), 364\u2013377 (2012)","journal-title":"J. Spacecr. Rocket."},{"issue":"5","key":"9821_CR38","doi-asserted-by":"publisher","first-page":"821","DOI":"10.1137\/0722050","volume":"22","author":"J Nocedal","year":"1985","unstructured":"Nocedal, J., Overton, M.L.: Projected Hessian updating algorithms for nonlinearly constrained optimization. SIAM J. Numer. Anal. 22(5), 821\u2013850 (1985)","journal-title":"SIAM J. Numer. Anal."},{"issue":"23","key":"9821_CR39","doi-asserted-by":"crossref","first-page":"138","DOI":"10.1080\/14786445208647087","volume":"4","author":"JJ Sylvester","year":"1852","unstructured":"Sylvester, J.J.: XIX. A demonstration of the theorem that every homogeneous quadratic polynomial is reducible by real orthogonal substitutions to the form of a sum of positive and negative squares. Lond. Edinb. Dublin Philos. Magazine J. Sci. 4(23), 138\u2013142 (1852)","journal-title":"Lond. Edinb. Dublin Philos. Magazine J. Sci."},{"key":"9821_CR40","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1090\/qam\/10666","volume":"2","author":"K Levenberg","year":"1944","unstructured":"Levenberg, K.: A method for the solution of certain problems in least squares. Q. Appl. Math. 2, 164\u2013168 (1944)","journal-title":"Q. Appl. Math."},{"issue":"1","key":"9821_CR41","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1007\/s10107-004-0559-y","volume":"106","author":"A W\u00e4chter","year":"2006","unstructured":"W\u00e4chter, A., Biegler, L.T.: On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Math. Progr. 106(1), 25\u201357 (2006)","journal-title":"Math. Progr."},{"key":"9821_CR42","unstructured":"Duff, I.S., Reid, J.K.: MA27\u2013a set of Fortran subroutines for solving sparse symmetric sets of linear equations. UKAEA Atomic Energy Research Establishment (1982)"},{"issue":"3","key":"9821_CR43","doi-asserted-by":"publisher","first-page":"302","DOI":"10.1145\/356044.356047","volume":"9","author":"IS Duff","year":"1983","unstructured":"Duff, I.S., Reid, J.K.: The multifrontal solution of indefinite sparse symmetric linear. ACM Trans. Math. Softw. (TOMS) 9(3), 302\u2013325 (1983)","journal-title":"ACM Trans. Math. Softw. (TOMS)"},{"issue":"1","key":"9821_CR44","doi-asserted-by":"publisher","first-page":"82","DOI":"10.1137\/1034004","volume":"34","author":"JW Liu","year":"1992","unstructured":"Liu, J.W.: The multifrontal method for sparse matrix solution: theory and practice. SIAM Rev. 34(1), 82\u2013109 (1992)","journal-title":"SIAM Rev."},{"key":"9821_CR45","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898718577","volume-title":"Practical Methods for Optimal Control and Estimation Using Nonlinear Programming","author":"JT Betts","year":"2010","unstructured":"Betts, J.T.: Practical Methods for Optimal Control and Estimation Using Nonlinear Programming, vol. 19. SIAM Press, Philadelphia (2010)"},{"issue":"2","key":"9821_CR46","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1002\/oca.739","volume":"25","author":"YJ Zhao","year":"2004","unstructured":"Zhao, Y.J.: Optimal patterns of glider dynamic soaring. Optim. Control Appl. Methods 25(2), 67\u201389 (2004)","journal-title":"Optim. Control Appl. Methods"},{"key":"9821_CR47","doi-asserted-by":"publisher","first-page":"809","DOI":"10.1038\/105809a0","volume":"105","author":"RH Goddard","year":"1920","unstructured":"Goddard, R.H.: A method of reaching extreme altitudes. Nature 105, 809\u2013811 (1920)","journal-title":"Nature"},{"issue":"1","key":"9821_CR48","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1002\/oca.814","volume":"29","author":"U Ledzewicz","year":"2008","unstructured":"Ledzewicz, U., Sch\u00e4ttler, H.: Analysis of optimal controls for a mathematical model of tumour anti-angiogenesis. Optim. Control Appl. Methods 29(1), 41\u201357 (2008)","journal-title":"Optim. Control Appl. Methods"},{"key":"9821_CR49","volume-title":"Applied Optimal Control: Optimization, Estimation, and Control","author":"AE Bryson","year":"1975","unstructured":"Bryson, A.E.: Applied Optimal Control: Optimization, Estimation, and Control. CRC Press, New York (1975)"},{"key":"9821_CR50","volume-title":"Combining Direct and Indirect Methods in Optimal Control: Range Maximization of a Hang Glider","author":"R Bulirsch","year":"1993","unstructured":"Bulirsch, R., Nerz, E., Pesch, H.J., von Stryk, O.: Combining Direct and Indirect Methods in Optimal Control: Range Maximization of a Hang Glider. Springer, Berlin (1993)"},{"issue":"5","key":"9821_CR51","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1002\/(SICI)1099-1514(199909\/10)20:5<235::AID-OCA658>3.0.CO;2-I","volume":"20","author":"Y Sakawa","year":"1999","unstructured":"Sakawa, Y.: Trajectory planning of a free-flying robot by using the optimal control. Optim. Control Appl. Methods 20(5), 235\u2013248 (1999)","journal-title":"Optim. Control Appl. Methods"},{"issue":"11","key":"9821_CR52","doi-asserted-by":"publisher","first-page":"1801","DOI":"10.1109\/PROC.1967.6011","volume":"55","author":"WF Tinney","year":"1967","unstructured":"Tinney, W.F., Walker, J.W.: Direct solutions of sparse network equations by optimally ordered triangular factorization. Proc. IEEE 55(11), 1801\u20131809 (1967)","journal-title":"Proc. IEEE"},{"issue":"4","key":"9821_CR53","doi-asserted-by":"publisher","first-page":"886","DOI":"10.1137\/S0895479894278952","volume":"17","author":"TA Davis","year":"1996","unstructured":"Davis, T.A., Amestoy, P., Duff, I.S.: An approximate minimum degree ordering algorithm. SIAM J. Matrix Anal. Appl. 17(4), 886\u2013905 (1996)","journal-title":"SIAM J. Matrix Anal. Appl."},{"issue":"2","key":"9821_CR54","doi-asserted-by":"publisher","first-page":"345","DOI":"10.1137\/0710032","volume":"10","author":"A George","year":"1973","unstructured":"George, A.: Nested dissection of a regular finite element mesh. SIAM J. Numer. Anal. 10(2), 345\u2013363 (1973)","journal-title":"SIAM J. Numer. Anal."},{"issue":"2","key":"9821_CR55","doi-asserted-by":"publisher","first-page":"236","DOI":"10.1137\/0713023","volume":"13","author":"NE Gibbs","year":"1976","unstructured":"Gibbs, N.E., Poole Jr, W.G., Stockmeyer, P.K.: An algorithm for reducing the bandwidth and profile of a sparse matrix. SIAM J. Numer. Anal. 13(2), 236\u2013250 (1976)","journal-title":"SIAM J. Numer. Anal."},{"issue":"1","key":"9821_CR56","doi-asserted-by":"publisher","first-page":"8","DOI":"10.1007\/BF01933580","volume":"20","author":"W-M Chan","year":"1980","unstructured":"Chan, W.-M., George, A.: A linear time implementation of the reverse Cuthill-McKee algorithm. BIT Numer. Math. 20(1), 8\u201314 (1980)","journal-title":"BIT Numer. Math."},{"issue":"3","key":"9821_CR57","doi-asserted-by":"publisher","first-page":"381","DOI":"10.1145\/1024074.1024081","volume":"30","author":"PR Amestoy","year":"2004","unstructured":"Amestoy, P.R., Davis, T.A., Duff, I.S.: Algorithm 837: AMD, an approximate minimum degree ordering algorithm. ACM Trans. Math. Softw. 30(3), 381\u2013388 (2004)","journal-title":"ACM Trans. Math. Softw."},{"issue":"1","key":"9821_CR58","first-page":"1","volume":"38","author":"TA Davis","year":"2011","unstructured":"Davis, T.A., Hu, Y.: The University of Florida sparse matrix collection. ACM Trans. Math. Softw. (TOMS) 38(1), 1 (2011)","journal-title":"ACM Trans. Math. Softw. (TOMS)"},{"key":"9821_CR59","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898718881","volume-title":"Direct Methods for Sparse Linear Systems","author":"TA Davis","year":"2006","unstructured":"Davis, T.A.: Direct Methods for Sparse Linear Systems, vol. 2. SIAM Press, Philadelphia (2006)"}],"container-title":["Computational Optimization and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-015-9821-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10589-015-9821-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-015-9821-x","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-015-9821-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,1]],"date-time":"2025-06-01T02:04:40Z","timestamp":1748743480000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10589-015-9821-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,1,6]]},"references-count":59,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2016,7]]}},"alternative-id":["9821"],"URL":"https:\/\/doi.org\/10.1007\/s10589-015-9821-x","relation":{},"ISSN":["0926-6003","1573-2894"],"issn-type":[{"type":"print","value":"0926-6003"},{"type":"electronic","value":"1573-2894"}],"subject":[],"published":{"date-parts":[[2016,1,6]]},"assertion":[{"value":"14 April 2015","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 January 2016","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}