{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,14]],"date-time":"2026-01-14T16:20:41Z","timestamp":1768407641780,"version":"3.49.0"},"reference-count":38,"publisher":"Springer Science and Business Media LLC","issue":"2-4","license":[{"start":{"date-parts":[[2011,7,21]],"date-time":"2011-07-21T00:00:00Z","timestamp":1311206400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Adv Comput Math"],"published-print":{"date-parts":[[2011,11]]},"DOI":"10.1007\/s10444-011-9173-8","type":"journal-article","created":{"date-parts":[[2011,7,20]],"date-time":"2011-07-20T13:19:21Z","timestamp":1311167961000},"page":"149-173","source":"Crossref","is-referenced-by-count":38,"title":["A preconditioning technique for a class of PDE-constrained optimization problems"],"prefix":"10.1007","volume":"35","author":[{"given":"Michele","family":"Benzi","sequence":"first","affiliation":[]},{"given":"Eldad","family":"Haber","sequence":"additional","affiliation":[]},{"given":"Lauren","family":"Taralli","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2011,7,21]]},"reference":[{"key":"9173_CR1","doi-asserted-by":"crossref","unstructured":"Akcelik, V., Biros, G., Ghattas, O.: Parallel multiscale Gauss\u2013Newton\u2013Krylov methods for inverse wave propagation. In: Proceedings of the IEEE\/ACM Conference, pp.\u00a01\u201315 (2002)","DOI":"10.1109\/SC.2002.10002"},{"key":"9173_CR2","doi-asserted-by":"crossref","unstructured":"Akcelik, V., Biros, G., Ghattas, O., et al.: High resolution forward and inverse earthquake modeling on terascale computers. In: Proceedings of the IEEE\/ACM Conference, pp.\u00a01\u201352 (2003)","DOI":"10.1145\/1048935.1050202"},{"key":"9173_CR3","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1137\/S0036141002410927","volume":"35","author":"S Angenent","year":"2003","unstructured":"Angenent, S., Haker, S., Tannenbaum, A.: Minimizing flows for the Monge\u2013Kantorovich problem. SIAM J. Math. Anal. 35, 61\u201397 (2003)","journal-title":"SIAM J. Math. Anal."},{"key":"9173_CR4","doi-asserted-by":"crossref","first-page":"R41","DOI":"10.1088\/0266-5611\/15\/2\/022","volume":"15","author":"SR Arridge","year":"1999","unstructured":"Arridge, S.R.: Optical tomography in medical imaging. Inverse Probl. 15, R41\u2013R93 (1999)","journal-title":"Inverse Probl."},{"key":"9173_CR5","doi-asserted-by":"crossref","first-page":"571","DOI":"10.1088\/0266-5611\/17\/3\/314","volume":"17","author":"UM Ascher","year":"2001","unstructured":"Ascher, U.M., Haber, E.: Grid refinement and scaling for distributed parameter estimation problems. Inverse Probl. 17, 571\u2013590 (2001)","journal-title":"Inverse Probl."},{"key":"9173_CR6","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1007\/s002110050002","volume":"84","author":"JD Benamou","year":"2000","unstructured":"Benamou, J.D., Brenier, Y.: A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem. Numer.\u00a0Math. 84, 375\u2013393 (2000)","journal-title":"Numer.\u00a0Math."},{"key":"9173_CR7","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1017\/S0962492904000212","volume":"14","author":"M Benzi","year":"2005","unstructured":"Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numer. 14, 1\u2013137 (2005)","journal-title":"Acta Numer."},{"key":"9173_CR8","volume-title":"Lecture Notes in Computational Science and Engineering, vol. 30","author":"L Biegler","year":"2003","unstructured":"Biegler, L., Ghattas, O., Heinkenschloss, M., Waanders, B.: Large-scale PDE-constrained optimization. In: Lecture Notes in Computational Science and Engineering, vol. 30. Springer, New York (2003)"},{"key":"9173_CR9","doi-asserted-by":"crossref","first-page":"687","DOI":"10.1137\/S106482750241565X","volume":"27","author":"G Biros","year":"2005","unstructured":"Biros, G., Ghattas, O.; Parallel Lagrange\u2013Newton\u2013Krylov\u2013Schur methods for PDE-constrained optimization. Parts I\u2013II. SIAM J. Sci. Comput. 27, 687\u2013738 (2005)","journal-title":"SIAM J. Sci. Comput."},{"key":"9173_CR10","doi-asserted-by":"crossref","first-page":"R95","DOI":"10.1088\/0266-5611\/15\/3\/201","volume":"116","author":"I Bouchouev","year":"1999","unstructured":"Bouchouev, I., Isakov, V.: Uniqueness, stability and numerical methods for the inverse problem that arises in financial markets. Inverse Probl. 15, R95\u2013R116 (1999)","journal-title":"Inverse Probl."},{"key":"9173_CR11","doi-asserted-by":"crossref","first-page":"1412","DOI":"10.1088\/0957-0233\/15\/7\/025","volume":"15","author":"R Casanova","year":"2004","unstructured":"Casanova, R., Silva, A., Borges, A.R.: A quantitative algorithm for parameter estimation in magnetic induction tomography. Meas. Sci. Technol. 15, 1412\u20131419 (2004)","journal-title":"Meas. Sci. Technol."},{"key":"9173_CR12","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1137\/S0036144598333613","volume":"41","author":"M Cheney","year":"1999","unstructured":"Cheney, M., Isaacson, D., Newell, J.C.: Electrical impedance tomography. SIAM Rev. 41, 85\u2013101 (1999)","journal-title":"SIAM Rev."},{"key":"9173_CR13","doi-asserted-by":"crossref","first-page":"1395","DOI":"10.1137\/0729080","volume":"29","author":"P Deuflhard","year":"1992","unstructured":"Deuflhard, P., Potra, F.: Asymptotic mesh independence of Newton-Galerkin methods via a refined Mysovskii theorem. SIAM J. Numer. Anal. 29, 1395\u20131412 (1992)","journal-title":"SIAM J. Numer. Anal."},{"key":"9173_CR14","unstructured":"Dollar, H.S.: Properties of Linear Systems in PDE-Constrained Optimization. Part I: Distributed Control. Tech.\u00a0Rep. RAL-TR-2009-017, Rutherford Appleton Laboratory (2009)"},{"key":"9173_CR15","first-page":"32","volume":"7","author":"B Dupire","year":"1994","unstructured":"Dupire, B.: Pricing with a smile. Risk 7, 32\u201339 (1994)","journal-title":"Risk"},{"key":"9173_CR16","doi-asserted-by":"crossref","first-page":"1027","DOI":"10.1088\/0266-5611\/21\/3\/014","volume":"21","author":"H Egger","year":"2005","unstructured":"Egger, H., Engl, H.W.: Tikhonov regularization applied to the inverse problem of option pricing: convergence analysis and rates. Inverse Probl. 21, 1027\u20131045 (2005)","journal-title":"Inverse Probl."},{"key":"9173_CR17","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198528678.001.0001","volume-title":"Finite Elements and Fast Iterative Solvers with Applications in Incompressible Fluid Dynamics","author":"H Elman","year":"2005","unstructured":"Elman, H., Silvester, D., Wathen, A.: Finite Elements and Fast Iterative Solvers with Applications in Incompressible Fluid Dynamics. Oxford University Press, Oxford (2005)"},{"key":"9173_CR18","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1046\/j.1365-2478.2001.00267.x","volume":"49","author":"G El-Qady","year":"2001","unstructured":"El-Qady, G., Ushijima, K.: Inversion of DC resistivity data using neural networks. Geophys. Prospect. 49, 417\u2013430 (2001)","journal-title":"Geophys. Prospect."},{"key":"9173_CR19","volume-title":"Matrix Computations","author":"GH Golub","year":"1996","unstructured":"Golub, G.H., Van\u00a0Loan, C.F.: Matrix Computations, 3rd edn. John Hopkins University Press, Baltimore (1996)","edition":"3"},{"key":"9173_CR20","doi-asserted-by":"crossref","first-page":"1847","DOI":"10.1088\/0266-5611\/17\/6\/319","volume":"17","author":"E Haber","year":"2001","unstructured":"Haber, E., Ascher, U.M.: Preconditioned all-at-once methods for large, sparse parameter estimation problems. Inverse Probl. 17, 1847\u20131864 (2001)","journal-title":"Inverse Probl."},{"key":"9173_CR21","doi-asserted-by":"crossref","first-page":"1594","DOI":"10.1137\/040608106","volume":"27","author":"E Haber","year":"2006","unstructured":"Haber, E., Modersitzki, J.: A multilevel method for image registration. SIAM J. Sci. Comput. 27, 1594\u20131607 (2006)","journal-title":"SIAM J. Sci. Comput."},{"key":"9173_CR22","unstructured":"Hanson, L.R.: Techniques in Constrained Optimization Involving Partial Differential Equations. PhD thesis, Emory University, Atlanta, GA (2007)"},{"key":"9173_CR23","unstructured":"Hu, J., Sala, M., Tong, C., Tuminaro, R., et al.: ML: Multilevel Preconditioning Package, The Trilinos Project, Sandia National Laboratories (2006). http:\/\/trilinos.sandia.gov\/packages\/ml\/"},{"key":"9173_CR24","doi-asserted-by":"crossref","first-page":"1381","DOI":"10.1007\/s10958-006-0049-2","volume":"133","author":"LV Kantorovich","year":"2006","unstructured":"Kantorovich, L.V.: On the translocation of masses. Dokl. Akad. Nauk SSSR 37, 227\u2013229 (1942) (in Russian). English translation in J. Math. Sci. 133, 1381\u20131382 (2006)","journal-title":"J. Math. Sci."},{"key":"9173_CR25","doi-asserted-by":"crossref","first-page":"1383","DOI":"10.1007\/s10958-006-0050-9","volume":"133","author":"LV Kantorovich","year":"2006","unstructured":"Kantorovich, L.V.: On a problem of Monge. Usp. Mat. Nauk 3, 225\u2013226 (1948) (in Russian). English translation in J. Math.\u00a0Sci. 133, 1383 (2006)","journal-title":"J. Math.\u00a0Sci."},{"key":"9173_CR26","doi-asserted-by":"crossref","first-page":"1763","DOI":"10.1137\/S0036139998334172","volume":"59","author":"MV Klibanov","year":"1999","unstructured":"Klibanov, M.V., Lucas, T.R.: Numerical solution of a parabolic inverse problem in optical tomography using experimental data. SIAM J. Appl. Math. 59, 1763\u20131789 (1999)","journal-title":"SIAM J. Appl. Math."},{"key":"9173_CR27","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1061\/(ASCE)0733-9496(2005)131:2(125)","volume":"131","author":"CD Laird","year":"2005","unstructured":"Laird, C.D., Biegler, L.T., Waanders, B., Bartlett, R.A.: Time-dependent contaminant source determination for municipal water networks using large scale optimization. ASCE J. Water Resour. Manage. Plan. 131, 125\u2013134 (2005)","journal-title":"ASCE J. Water Resour. Manage. Plan."},{"key":"9173_CR28","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-0348-5116-9","volume-title":"Numerical Methods for Conservation Laws","author":"RJ LeVeque","year":"1990","unstructured":"LeVeque, R.J.: Numerical Methods for Conservation Laws. Birkhauser, New York (1990)"},{"key":"9173_CR29","doi-asserted-by":"crossref","DOI":"10.1007\/b98874","volume-title":"Numerical Optimization","author":"J Nocedal","year":"1999","unstructured":"Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, New York (1999)"},{"key":"9173_CR30","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1016\/0956-0521(92)90116-Z","volume":"1","author":"C Orozco","year":"1992","unstructured":"Orozco, C., Ghattas, O.; Massively parallel aerodynamic shape optimization. Comput. Syst. Eng. 1, 311\u2013320 (1992)","journal-title":"Comput. Syst. Eng."},{"key":"9173_CR31","doi-asserted-by":"crossref","DOI":"10.1515\/9780691206837","volume-title":"Geophysical Inverse Theory","author":"RL Parker","year":"1994","unstructured":"Parker, R.L.: Geophysical Inverse Theory. Princeton University Press, Princeton (1994)"},{"key":"9173_CR32","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1137\/080727154","volume":"32","author":"T Rees","year":"2010","unstructured":"Rees, T., Dollar, H.S., Wathen, A.J.: Optimal solvers for PDE-constrained optimization. SIAM J. Sci. Comput. 32, 271\u2013298 (2010)","journal-title":"SIAM J. Sci. Comput."},{"key":"9173_CR33","doi-asserted-by":"crossref","first-page":"977","DOI":"10.1002\/nla.693","volume":"17","author":"T Rees","year":"2010","unstructured":"Rees, T., Stoll, M.: Block-triangular preconditioners for PDE-constrained optimization. Numer. Linear Algebra Appl. 17, 977\u2013996 (2010). doi: 10.1002\/nla.693","journal-title":"Numer. Linear Algebra Appl."},{"key":"9173_CR34","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1137\/0914028","volume":"14","author":"Y Saad","year":"1993","unstructured":"Saad, Y.: A flexible inner-outer preconditioned GMRES algorithm. SIAM J. Sci. Comput. 14, 451\u2013469 (1993)","journal-title":"SIAM J. Sci. Comput."},{"key":"9173_CR35","doi-asserted-by":"crossref","first-page":"856","DOI":"10.1137\/0907058","volume":"7","author":"Y Saad","year":"1986","unstructured":"Saad, Y., Schultz, M.H.: GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comput. 7, 856\u2013869 (1986)","journal-title":"SIAM J. Sci. Stat. Comput."},{"key":"9173_CR36","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1080\/10618569808940863","volume":"11","author":"A Shenoy","year":"1998","unstructured":"Shenoy, A., Heinkenschloss, M., Cliff, E.M.: Airfoil design by an all-at-once method. Int. J. Comput. Fluid Dyn. 11, 3\u201325 (1998)","journal-title":"Int. J. Comput. Fluid Dyn."},{"key":"9173_CR37","doi-asserted-by":"crossref","first-page":"1027","DOI":"10.1137\/S0895479897317703","volume":"20","author":"CR Vogel","year":"1999","unstructured":"Vogel, C.R.: Sparse matrix computations arising in distributed parameter identification. SIAM J. Matrix Anal. Appl. 20, 1027\u20131037 (1999)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"9173_CR38","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898717570","volume-title":"Computational Methods for Inverse Problems, Frontiers in Applied Mathematics Series","author":"CR Vogel","year":"2002","unstructured":"Vogel, C.R.: Computational Methods for Inverse Problems, Frontiers in Applied Mathematics Series. Society for Industrial and Applied Mathematics, Philadelphia (2002)"}],"container-title":["Advances in Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-011-9173-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10444-011-9173-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-011-9173-8","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,4,8]],"date-time":"2024-04-08T22:26:56Z","timestamp":1712615216000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10444-011-9173-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,7,21]]},"references-count":38,"journal-issue":{"issue":"2-4","published-print":{"date-parts":[[2011,11]]}},"alternative-id":["9173"],"URL":"https:\/\/doi.org\/10.1007\/s10444-011-9173-8","relation":{},"ISSN":["1019-7168","1572-9044"],"issn-type":[{"value":"1019-7168","type":"print"},{"value":"1572-9044","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,7,21]]}}}