{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,22]],"date-time":"2026-08-22T09:19:48Z","timestamp":1787390388521,"version":"3.56.0"},"reference-count":31,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[1997,1,1]],"date-time":"1997-01-01T00:00:00Z","timestamp":852076800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Programming"],"published-print":{"date-parts":[[1997,1]]},"DOI":"10.1007\/bf02614383","type":"journal-article","created":{"date-parts":[[2007,4,28]],"date-time":"2007-04-28T00:38:07Z","timestamp":1177720687000},"page":"183-210","source":"Crossref","is-referenced-by-count":19,"title":["A QMR-based interior-point algorithm for solving linear programs"],"prefix":"10.1007","volume":"76","author":[{"given":"Roland W.","family":"Freund","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Florian","family":"Jarre","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","reference":[{"key":"BF02614383_CR1","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1007\/BF01587095","volume":"44","author":"I. Adler","year":"1989","unstructured":"I. Adler, N.K. Karmarkar, M.G.C. Resende and G. Veiga, \u201cAn implementation of Karmarkar\u2019s algorithm for linear programming,\u201dMathematical Programming 44 (1989) 297\u2013335.","journal-title":"Mathematical Programming"},{"key":"BF02614383_CR2","doi-asserted-by":"crossref","first-page":"166","DOI":"10.1007\/BF01934996","volume":"25","author":"O. Axelsson","year":"1985","unstructured":"O. Axelsson, \u201cA survey of preconditioned iterative methods for linear systems of algebraic equations,\u201dBIT 25 (1985) 166\u2013187.","journal-title":"BIT"},{"key":"BF02614383_CR3","doi-asserted-by":"crossref","first-page":"639","DOI":"10.1137\/0708060","volume":"8","author":"J.R. Bunch","year":"1971","unstructured":"J.R. Bunch and B.N. Parlett, \u201cDirect methods for solving symmetric indefinite systems of linear equations,\u201dSIAM Journal on Numerical Analysis 8 (1971) 639\u2013655.","journal-title":"SIAM Journal on Numerical Analysis"},{"key":"BF02614383_CR4","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1137\/0902001","volume":"2","author":"S.C. Eisenstat","year":"1981","unstructured":"S.C. Eisenstat, \u201cEfficient implementation of a class of preconditioned conjugate gradient methods,\u201dSIAM Journal on Scientific and Statistical Computing 2 (1981) 1\u20134.","journal-title":"SIAM Journal on Scientific and Statistical Computing"},{"key":"BF02614383_CR5","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1007\/BF01585158","volume":"62","author":"R. Fourer","year":"1993","unstructured":"R. Fourer and S. Mehrotra, \u201cSolving symmetric indefinite systems in an interior-point method for linear programming,\u201dMathematical Programming 62 (1993) 15\u201339.","journal-title":"Mathematical Programming"},{"key":"BF02614383_CR6","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1007\/978-3-0348-8619-2_5","volume-title":"Numerical Methods of Approximation Theory","author":"R.W. Freund","year":"1992","unstructured":"R.W. Freund, \u201cQuasi-kernel polynomials and convergence results for quasi-minimal residual iterations,\u201d in: D. Braess and L. Schumaker, eds.,Numerical Methods of Approximation Theory (Birkha\u00fcser, Basel, 1992) pp. 77\u201395."},{"key":"BF02614383_CR7","series-title":"The IMA Volumes in Mathematics and its Applications","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1007\/978-1-4613-9353-5_6","volume-title":"Recent Advances in Iterative Methods","author":"R.W. Freund","year":"1994","unstructured":"R.W. Freund, \u201cTranspose-free quasi-minimal residual methods for non-Hermitian linear systems,\u201d in: G. Golub, A. Greenbaum, and M. Luskin, eds.,Recent Advances in Iterative Methods, The IMA Volumes in Mathematics and its Applications, Vol. 60 (Springer, New York, 1994) pp. 69\u201394."},{"key":"BF02614383_CR8","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1017\/S0962492900002245","volume":"1","author":"R.W. Freund","year":"1992","unstructured":"R.W. Freund, G.H. Golub and N.M. Nachtigal, \u201cIterative solution of linear systems,\u201dActa Numerica 1 (1992) 57\u2013100.","journal-title":"Acta Numerica"},{"key":"BF02614383_CR9","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1137\/0914009","volume":"14","author":"R.W. Freund","year":"1993","unstructured":"R.W. Freund, M.H. Gutknecht and N.M. Nachtigal, \u201cAn implementation of the look-ahead Lanczos algorithm for non-Hermitian matrices,\u201dSIAM Journal on Scientific Computing 14 (1993) 137\u2013158.","journal-title":"SIAM Journal on Scientific Computing"},{"key":"BF02614383_CR10","series-title":"Numerical Analysis Manuscript","volume-title":"Convergence of a class of inexact interior-point algorithms for linear programs","author":"R.W. Freund","year":"1996","unstructured":"R.W. Freund, F. Jarre and S. Mizuno, \u201cConvergence of a class of inexact interior-point algorithms for linear programs,\u201d Numerical Analysis Manuscript 96-16, Bell Laboratories, Murray Hill, NJ (1996)."},{"key":"BF02614383_CR11","series-title":"Numerical Analysis Manuscript","volume-title":"Numerical experiences with a QMR-based interior-point algorithm for linear programs","author":"R.W. Freund","year":"1996","unstructured":"R.W. Freund and F. Jarre, \u201cNumerical experiences with a QMR-based interior-point algorithm for linear programs,\u201d Numerical Analysis Manuscript, Bell Laboratories, Murray Hill, NJ (1996), in preparation."},{"key":"BF02614383_CR12","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1007\/BF01385726","volume":"60","author":"R.W. Freund","year":"1991","unstructured":"R.W. Freund and N.M. Nachtigal, \u201cQMR: A quasi-minimal residual method for non-Hermitian linear systems,\u201dNumerische Mathematik 60 (1991) 315\u2013339.","journal-title":"Numerische Mathematik"},{"key":"BF02614383_CR13","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1137\/0915022","volume":"15","author":"R.W. Freund","year":"1994","unstructured":"R.W. Freund and N.M. Nachtigal, \u201cAn implementation of the QMR method based on coupled two-term recurrences,\u201dSIAM Journal on Scientific Computing 15 (1994) 313\u2013337.","journal-title":"SIAM Journal on Scientific Computing"},{"key":"BF02614383_CR14","first-page":"258","volume-title":"Advances in Computer Methods for Partial Differential Equations \u2014 VII","author":"R.W. Freund","year":"1992","unstructured":"R.W. Freund and T. Szeto, \u201cA transpose-free quasi-minimal residual squared algorithm for non-Hermitian linear systems,\u201d in: R. Vichnevetsky, D. Knight and G. Richter, eds.,Advances in Computer Methods for Partial Differential Equations \u2014 VII (IMACS, New Brunswick, NJ, 1992) pp. 258\u2013264."},{"key":"BF02614383_CR15","volume-title":"Simplifications of the nonsymmetric Laczos process and a new algorithm for Hermitian indefinite linear systems","author":"R.W. Freund","year":"1995","unstructured":"R.W. Freund and H. Zha, \u201cSimplifications of the nonsymmetric Laczos process and a new algorithm for Hermitian indefinite linear systems,\u201d AT & T Numerical Analysis Manuscript, Bell Laboratories, Murray Hill, NJ (1995)."},{"key":"BF02614383_CR16","first-page":"10","volume":"13","author":"D.M. Gay","year":"1985","unstructured":"D.M. Gay, \u201cElectronic mail distribution of linear programming test problems,\u201dMathematical Programming Society COAL Newsletter 13 (1985) 10\u201312.","journal-title":"Mathematical Programming Society COAL Newsletter"},{"key":"BF02614383_CR17","doi-asserted-by":"crossref","first-page":"292","DOI":"10.1137\/0613022","volume":"13","author":"P.E. Gill","year":"1992","unstructured":"P.E. Gill, W. Murray, D.B. Poncele\u00f3n and M.A. Saunders, \u201cPreconditioners for indefinite systems arising in optimization,\u201dSIAM Journal on Matrix Analysis and Applications 13 (1992) 292\u2013311.","journal-title":"SIAM Journal on Matrix Analysis and Applications"},{"key":"BF02614383_CR18","doi-asserted-by":"crossref","first-page":"409","DOI":"10.6028\/jres.049.044","volume":"49","author":"M.R. Hestenes","year":"1952","unstructured":"M.R. Hestenes and E. Stiefel, \u201cMethods of conjugate gradients for solving linear systems,\u201dJournal of Research of the National Bureau of Standards 49 (1952) 409\u2013436.","journal-title":"Journal of Research of the National Bureau of Standards"},{"key":"BF02614383_CR19","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1007\/BF02579150","volume":"4","author":"N.K. Karmarkar","year":"1984","unstructured":"N.K. Karmarkar, \u201cA new polynomial-time algorithm for linear programming,\u201dCombinatorica 4 (1984) 373\u2013395.","journal-title":"Combinatorica"},{"key":"BF02614383_CR20","doi-asserted-by":"crossref","first-page":"555","DOI":"10.1007\/BF01582905","volume":"52","author":"N.K. Karmarkar","year":"1991","unstructured":"N.K. Karmarkar and K.G. Ramakrishnan. \u201cComputational results of an interior point algorithm for large scale linear programming,\u201dMathematical Programming 52 (1991) 555\u2013586.","journal-title":"Mathematical Programming"},{"key":"BF02614383_CR21","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1007\/BF01582151","volume":"61","author":"M. Kojima","year":"1993","unstructured":"M. Kojima, N. Megiddo and S. Mizuno. \u201cA primal-dual infeasible-interior-point algorithm for linear programming,\u201dMathematical Programming 61 (1993) 263\u2013280.","journal-title":"Mathematical Programming"},{"key":"BF02614383_CR22","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1007\/978-1-4613-9617-8_2","volume-title":"Progress in Mathematical Programming, Interior-Point and Related Methods","author":"M. Kojima","year":"1989","unstructured":"M. Kojima, S. Mizuno and A. Yoshise, \u201cA primal-dual interior point algorithm for linear programming,\u201d in: N. Megiddo, ed.,Progress in Mathematical Programming, Interior-Point and Related Methods (Springer, New York, 1989) pp. 29\u201347."},{"key":"BF02614383_CR23","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1016\/0024-3795(91)90275-2","volume":"152","author":"Lustig I.J.","year":"1991","unstructured":"I.J. Lustig, R.E. Marsten and D.F. Shanno, \u201cComputational experience with a primal-dual interior point method for linear programming,\u201dLinear Algebra and its Applications 152 (1991) 191\u2013222.","journal-title":"Linear Algebra and its Applications"},{"key":"BF02614383_CR24","doi-asserted-by":"crossref","first-page":"435","DOI":"10.1137\/0802022","volume":"2","author":"I.J. Lustig","year":"1992","unstructured":"I.J. Lustig, R.E. Marsten and D.F. Shanno, \u201cOn implementing Mehrotra\u2019s predictor-corrector interior-point method for linear programming,\u201dSIAM Journal on Optimization 2 (1992) 435\u2013449.","journal-title":"SIAM Journal on Optimization"},{"key":"BF02614383_CR25","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1007\/978-1-4613-9617-8_8","volume-title":"Progress in Mathematical Programming, Interior-Point and Related Methods","author":"N. Megiddo","year":"1989","unstructured":"N. Megiddo, \u201cPathways to the optimal set in linear programming,\u201d in: N. Negiddo, ed.,Progress in Mathematical Programming, Interior-Point and Related Methods (Springer, New York, 1989) pp. 131\u2013158."},{"key":"BF02614383_CR26","volume-title":"Implementation of a primal-dual path following method for solving large linear programs","author":"J. Menniken","year":"1991","unstructured":"J. Menniken, \u201cImplementation of a primal-dual path following method for solving large linear programs,\u201d Dissertation, Fakult\u00e4t f\u00fcr Mathematik und informatik, Universit\u00e4t W\u00fcrzburg, W\u00fcrzburg, Germany (1991)."},{"key":"BF02614383_CR27","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1007\/BF01587075","volume":"44","author":"R.D.C. Monteiro","year":"1989","unstructured":"R.D.C. Monteiro and I. Adler, \u201cInterior path following primal-dual algorithms. Part I: Linear programming,\u201dMathematical Programming 44 (1989) 27\u201341.","journal-title":"Mathematical Programming"},{"key":"BF02614383_CR28","doi-asserted-by":"crossref","first-page":"617","DOI":"10.1137\/0712047","volume":"12","author":"C.C. Paige","year":"1975","unstructured":"C.C. Paige and M.A. Saunders, \u201cSolution of sparse indefinite systems of linear equations,\u201dSIAM Journal on Numerical Analysis 12 (1975) 617\u2013629.","journal-title":"SIAM Journal on Numerical Analysis"},{"key":"BF02614383_CR29","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1007\/BFb0042787","volume-title":"System Modelling and Optimization","author":"K. Tanabe","year":"1988","unstructured":"K. Tanabe, \u201cCentered Newton method for mathematical programming,\u201d in: M. Iri and K. Yajima, eds.,System Modelling and Optimization (Springer, New York, 1988) pp. 197\u2013206."},{"key":"BF02614383_CR30","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF01581257","volume":"58","author":"R.J. Vanderbei","year":"1993","unstructured":"R.J. Vanderbei and T.J. Carpenter, \u201cSymmetric indefinite systems for interior point methods,\u201dMathematical Programming 58 (1993) 1\u201332.","journal-title":"Mathematical Programming"},{"key":"BF02614383_CR31","series-title":"Working Paper","volume-title":"A simplified homogeneous and self-dual linear programming algorithm and its implementation","author":"X. Xu","year":"1993","unstructured":"X. Xu, P.F. Hung and Y. Ye, \u201cA simplified homogeneous and self-dual linear programming algorithm and its implementation,\u201d Working Paper, College of Business Administration, The University of Iowa, Iowa City, IA (1993)."}],"container-title":["Mathematical Programming"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF02614383.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/BF02614383\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF02614383","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,15]],"date-time":"2025-01-15T18:19:22Z","timestamp":1736965162000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BF02614383"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1997,1]]},"references-count":31,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1997,1]]}},"alternative-id":["BF02614383"],"URL":"https:\/\/doi.org\/10.1007\/bf02614383","relation":{},"ISSN":["0025-5610","1436-4646"],"issn-type":[{"value":"0025-5610","type":"print"},{"value":"1436-4646","type":"electronic"}],"subject":[],"published":{"date-parts":[[1997,1]]}}}