{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,8,22]],"date-time":"2023-08-22T04:13:51Z","timestamp":1692677631918},"reference-count":29,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2016,11,30]],"date-time":"2016-11-30T00:00:00Z","timestamp":1480464000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comput Optim Appl"],"published-print":{"date-parts":[[2017,5]]},"DOI":"10.1007\/s10589-016-9887-0","type":"journal-article","created":{"date-parts":[[2016,11,30]],"date-time":"2016-11-30T05:05:46Z","timestamp":1480482346000},"page":"111-127","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["A new approach for finding a basis for the splitting preconditioner for linear systems from interior point methods"],"prefix":"10.1007","volume":"67","author":[{"given":"Porfirio","family":"Su\u00f1agua","sequence":"first","affiliation":[]},{"given":"Aurelio R. L.","family":"Oliveira","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2016,11,30]]},"reference":[{"issue":"3","key":"9887_CR1","doi-asserted-by":"crossref","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. (TOMS) 30(3), 381\u2013388 (2004)","journal-title":"ACM Trans. Math. Softw. (TOMS)"},{"issue":"2","key":"9887_CR2","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1023\/B:COAP.0000026882.34332.1b","volume":"28","author":"L Bergamaschi","year":"2004","unstructured":"Bergamaschi, L., Gondzio, J., Zilli, G.: Preconditioning indefinite systems in interior point methods for optimization. Comput. Optim. Appl. 28(2), 149\u2013171 (2004)","journal-title":"Comput. Optim. Appl."},{"issue":"2\u20133","key":"9887_CR3","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1007\/s10589-006-9009-5","volume":"36","author":"S Bocanegra","year":"2007","unstructured":"Bocanegra, S., Campos, F., Oliveira, A.R.: Using a hybrid preconditioner for solving large-scale linear systems arising from interior point methods. Comput. Optim. Appl. 36(2\u20133), 149\u2013164 (2007)","journal-title":"Comput. Optim. Appl."},{"key":"9887_CR4","unstructured":"Campos, F.F., Rollet, J.S.: Controlled Cholesky Factorization for Preconditioning the Conjugate Gradient Method. Oxford University Computing Laboratory, Numerical Analysis Group (1995)"},{"issue":"2","key":"9887_CR5","doi-asserted-by":"crossref","first-page":"240","DOI":"10.1287\/opre.38.2.240","volume":"38","author":"WJ Carolan","year":"1990","unstructured":"Carolan, W.J., Hill, J.E., Kennington, J.L., Niemi, S., Wichmann, S.J.: An empirical evaluation of the korbx $$\\textregistered $$ \u00ae algorithms for military airlift applications. Oper. Res. 38(2), 240\u2013248 (1990)","journal-title":"Oper. Res."},{"key":"9887_CR6","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1007\/s10589-006-9006-8","volume":"36","author":"J Chai","year":"2007","unstructured":"Chai, J., Toh, K.: Preconditioning and iterative solution of symmetric indefinite linear system arising from interior point methods for linear programming. Comput. Optim. Appl. 36, 221\u2013247 (2007)","journal-title":"Comput. Optim. Appl."},{"issue":"1\u20134","key":"9887_CR7","doi-asserted-by":"crossref","first-page":"397","DOI":"10.1080\/10556789908805757","volume":"11\u20132","author":"J Czyzyk","year":"1999","unstructured":"Czyzyk, J., Mehrotra, S., Wagner, M., Wright, S.J.: PCx an interior point code for linear programming. Optim. Methods Softw. 11\u20132(1\u20134), 397\u2013430 (1999)","journal-title":"Optim. Methods Softw."},{"issue":"2","key":"9887_CR8","doi-asserted-by":"crossref","first-page":"196","DOI":"10.1145\/992200.992206","volume":"30","author":"TA Davis","year":"2004","unstructured":"Davis, T.A.: Algorithm 832: Umfpack v4. 3\u2014an unsymmetric-pattern multifrontal method. ACM Trans. Math. Softw. (TOMS) 30(2), 196\u2013199 (2004)","journal-title":"ACM Trans. Math. Softw. (TOMS)"},{"issue":"1","key":"9887_CR9","doi-asserted-by":"crossref","first-page":"140","DOI":"10.1137\/S0895479894246905","volume":"18","author":"TA Davis","year":"1997","unstructured":"Davis, T.A., Duff, I.S.: An unsymmetric-pattern multifrontal method for sparse lu factorization. SIAM J. Matrix Anal. Appl. 18(1), 140\u2013158 (1997)","journal-title":"SIAM J. Matrix Anal. Appl."},{"issue":"2","key":"9887_CR10","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1007\/s101070100263","volume":"91","author":"ED Dolan","year":"2002","unstructured":"Dolan, E.D., More, J.J.: Benchmarking optimization software with performance profiles. Math. Program. 91(2), 201\u2013213 (2002)","journal-title":"Math. Program."},{"issue":"3","key":"9887_CR11","doi-asserted-by":"crossref","first-page":"557","DOI":"10.1007\/s10589-015-9735-7","volume":"61","author":"MD Drazic","year":"2015","unstructured":"Drazic, M.D., Lazovic, R.P., Kovacevic-Vujcic, V.V.: Sparsity preserving preconditioners for linear systems in interior-point methods. Comput. Optim. Appl. 61(3), 557\u2013570 (2015)","journal-title":"Comput. Optim. Appl."},{"issue":"2","key":"9887_CR12","doi-asserted-by":"crossref","first-page":"118","DOI":"10.1145\/992200.992202","volume":"30","author":"IS Duff","year":"2004","unstructured":"Duff, I.S.: Ma57\u2013a code for the solution of sparse symmetric definite and indefinite systems. ACM Trans. Math. Softw. (TOMS) 30(2), 118\u2013144 (2004)","journal-title":"ACM Trans. Math. Softw. (TOMS)"},{"issue":"3","key":"9887_CR13","doi-asserted-by":"crossref","first-page":"1007","DOI":"10.1137\/050629598","volume":"29","author":"IS Duff","year":"2007","unstructured":"Duff, I.S., Pralet, S.: Towards stable mixed pivoting strategies for the sequential and parallel solution of sparse symmetric indefinite systems. SIAM J. Matrix Anal. Appl. 29(3), 1007\u20131024 (2007)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"9887_CR14","doi-asserted-by":"crossref","first-page":"1267","DOI":"10.1016\/j.laa.2011.08.023","volume":"218","author":"CTLS Ghidini","year":"2012","unstructured":"Ghidini, C.T.L.S., Oliveira, A.R.L., Silva, J., Velazco, M.I.: Combining a hybrid preconditioner and a optimal adjustment algorithm to accelerate the convergence of interior point methods. Linear Algebra Appl. 218, 1267\u20131284 (2012)","journal-title":"Linear Algebra Appl."},{"key":"9887_CR15","first-page":"45","volume":"3","author":"CTLS Ghidini","year":"2014","unstructured":"Ghidini, C.T.L.S., Oliveira, A.R.L., Sorensen, D.C.: Computing a hybrid preconditioner approach to solve the linear systems arising from interior point methods for linear programming using the gradient conjugate method. Ann. Manag. Sci. 3, 45\u201366 (2014)","journal-title":"Ann. Manag. Sci."},{"key":"9887_CR16","doi-asserted-by":"crossref","DOI":"10.56021\/9781421407944","volume-title":"Matrix Computations","author":"GH Golub","year":"2013","unstructured":"Golub, G.H., Van Loan, C.F.: Matrix Computations. JHU Press, Baltimore (2013)"},{"issue":"3","key":"9887_CR17","doi-asserted-by":"crossref","first-page":"587","DOI":"10.1016\/j.ejor.2011.09.017","volume":"218","author":"J Gondzio","year":"2012","unstructured":"Gondzio, J.: Interior point methods 25 years later. Eur. J. Oper. Res. 218(3), 587\u2013601 (2012)","journal-title":"Eur. J. Oper. Res."},{"issue":"1","key":"9887_CR18","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1016\/0021-9991(78)90098-0","volume":"26","author":"DS Kershaw","year":"1978","unstructured":"Kershaw, D.S.: The incomplete cholesky-conjugate gradient method for the iterative solution of systems of linear equations. J. Comput. Phys. 26(1), 43\u201365 (1978)","journal-title":"J. Comput. Phys."},{"key":"9887_CR19","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"533","DOI":"10.1007\/978-3-642-40047-6_54","volume-title":"Euro-Par 2013 Parallel Processing","author":"A Kuzmin","year":"2013","unstructured":"Kuzmin, A., Luisier, M., Schenk, O.: Fast methods for computing selected elements of the greens function in massively parallel nanoelectronic device simulations. In: Wolf, F., Mohr, B., Mey, D. (eds.) Euro-Par 2013 Parallel Processing. Lecture Notes in Computer Science, vol. 8097, pp. 533\u2013544. Springer, Berlin (2013). doi: 10.1007\/978-3-642-40047-6_54"},{"key":"9887_CR20","volume-title":"Linear and Nonlinear Programming","author":"DG Luenberger","year":"2003","unstructured":"Luenberger, D.G.: Linear and Nonlinear Programming. Springer, New York (2003)"},{"issue":"3","key":"9887_CR21","doi-asserted-by":"crossref","first-page":"435","DOI":"10.1137\/0802022","volume":"2","author":"IJ Lustig","year":"1992","unstructured":"Lustig, I.J., Marsten, R.E., Shanno, D.F.: On implementing mehrotra\u2019s predictor-corrector interior-point method for linear programming. SIAM J. Optim. 2(3), 435\u2013449 (1992)","journal-title":"SIAM J. Optim."},{"issue":"3","key":"9887_CR22","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1287\/mnsc.3.3.255","volume":"3","author":"HM Markowitz","year":"1957","unstructured":"Markowitz, H.M.: The elimination form of the inverse and its application to linear programming. Manag. Sci. 3(3), 255\u2013269 (1957)","journal-title":"Manag. Sci."},{"key":"9887_CR23","doi-asserted-by":"crossref","first-page":"575","DOI":"10.1137\/0802028","volume":"2","author":"S Mehrotra","year":"1992","unstructured":"Mehrotra, S.: On the implementation of a primal-dual interior point method. SIAM J. Optim. 2, 575\u2013601 (1992)","journal-title":"SIAM J. Optim."},{"key":"9887_CR24","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.laa.2004.08.019","volume":"394","author":"AR Oliveira","year":"2005","unstructured":"Oliveira, A.R., Sorensen, D.C.: A new class of preconditioners for large-scale linear systems from interior point methods for linear programming. Linear Algebra Appl. 394, 1\u201324 (2005)","journal-title":"Linear Algebra Appl."},{"issue":"1","key":"9887_CR25","doi-asserted-by":"publisher","first-page":"91","DOI":"10.1137\/070707002","volume":"50","author":"O Schenk","year":"2008","unstructured":"Schenk, O., Bollh\u00f6fer, M., R\u00f6mer, R.A.: On large-scale diagonalization techniques for the Anderson model of localization. SIAM Rev. 50(1), 91\u2013112 (2008). doi: 10.1137\/070707002","journal-title":"SIAM Rev."},{"issue":"2\u20133","key":"9887_CR26","doi-asserted-by":"publisher","first-page":"321","DOI":"10.1007\/s10589-006-9003-y","volume":"36","author":"O Schenk","year":"2007","unstructured":"Schenk, O., W\u00e4chter, A., Hagemann, M.: Matching-based preprocessing algorithms to the solution of saddle-point problems in large-scale nonconvex interior-point optimization. Comput. Optim. Appl. 36(2\u20133), 321\u2013341 (2007). doi: 10.1007\/s10589-006-9003-y","journal-title":"Comput. Optim. Appl."},{"issue":"2","key":"9887_CR27","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1080\/10556780902992829","volume":"25","author":"M Velazco","year":"2010","unstructured":"Velazco, M., Oliveira, A.R., Campos, F.: A note on hybrid preconditioners for large-scale normal equations arising from interior-point methods. Optim. Methods Softw. 25(2), 321\u2013332 (2010)","journal-title":"Optim. Methods Softw."},{"key":"9887_CR28","doi-asserted-by":"crossref","unstructured":"Wright, S.J.: Primal-Dual Interior-Point Methods, vol.\u00a054. SIAM (1997)","DOI":"10.1137\/1.9781611971453"},{"issue":"1","key":"9887_CR29","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1137\/0602010","volume":"2","author":"M Yannakakis","year":"1981","unstructured":"Yannakakis, M.: Computing the minimum fill-in is NP-complete. SIAM J. Algebr. Discret. Methods 2(1), 77\u201379 (1981)","journal-title":"SIAM J. Algebr. Discret. Methods"}],"container-title":["Computational Optimization and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-016-9887-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10589-016-9887-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-016-9887-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,21]],"date-time":"2023-08-21T03:33:54Z","timestamp":1692588834000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10589-016-9887-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,11,30]]},"references-count":29,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2017,5]]}},"alternative-id":["9887"],"URL":"https:\/\/doi.org\/10.1007\/s10589-016-9887-0","relation":{},"ISSN":["0926-6003","1573-2894"],"issn-type":[{"value":"0926-6003","type":"print"},{"value":"1573-2894","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,11,30]]}}}