{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,26]],"date-time":"2026-06-26T01:54:31Z","timestamp":1782438871672,"version":"3.54.5"},"reference-count":36,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2017,1,13]],"date-time":"2017-01-13T00:00:00Z","timestamp":1484265600000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100003086","name":"Eusko Jaurlaritza","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100003086","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2017,7]]},"DOI":"10.1007\/s10915-016-0351-1","type":"journal-article","created":{"date-parts":[[2017,1,13]],"date-time":"2017-01-13T08:48:32Z","timestamp":1484297312000},"page":"198-230","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Boundary Treatment and Multigrid Preconditioning for Semi-Lagrangian Schemes Applied to Hamilton\u2013Jacobi\u2013Bellman Equations"],"prefix":"10.1007","volume":"72","author":[{"given":"Christoph","family":"Reisinger","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5776-1212","authenticated-orcid":false,"given":"Julen","family":"Rotaetxe Arto","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2017,1,13]]},"reference":[{"key":"351_CR1","unstructured":"Akian, M., S\u00e9quier, P., Sulem, A.: A finite horizon multidimensional portfolio selection problem with singular transactions. In: Proceedings of the 34th IEEE Conference on Decision and Control, 1995, vol\u00a03, pp. 2193\u20132198. IEEE (1995)"},{"issue":"3","key":"351_CR2","doi-asserted-by":"crossref","first-page":"271","DOI":"10.3233\/ASY-1991-4305","volume":"4","author":"G Barles","year":"1991","unstructured":"Barles, G., Souganidis, P.E.: Convergence of approximation schemes for fully nonlinear second order equations. Asymptot. Anal. 4(3), 271\u2013283 (1991)","journal-title":"Asymptot. Anal."},{"issue":"3\u20134","key":"351_CR3","first-page":"275","volume":"10","author":"M Blo\u00df","year":"1989","unstructured":"Blo\u00df, M., Hoppe, R.H.W.: Numerical computation of the value function of optimally controlled stochastic switching processes by multi-grid techniques. Numer. Funct. Anal. Optim. 10(3\u20134), 275\u2013304 (1989)","journal-title":"Numer. Funct. Anal. Optim."},{"issue":"4","key":"351_CR4","doi-asserted-by":"crossref","first-page":"3001","DOI":"10.1137\/08073041X","volume":"47","author":"O Bokanowski","year":"2009","unstructured":"Bokanowski, O., Maroso, S., Zidani, H.: Some convergence results for Howard\u2019s algorithm. SIAM J. Numer. Anal. 47(4), 3001\u20133026 (2009)","journal-title":"SIAM J. Numer. Anal."},{"issue":"1","key":"351_CR5","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1051\/m2an\/1995290100971","volume":"29","author":"F Camilli","year":"1995","unstructured":"Camilli, F., Falcone, M.: An approximation scheme for the optimal control of diffusion processes. ESAIM Math. Model. Numer. Anal. Mod\u00e9lisation Math\u00e9matique et Analyse Num\u00e9rique 29(1), 97\u2013122 (1995)","journal-title":"ESAIM Math. Model. Numer. Anal. Mod\u00e9lisation Math\u00e9matique et Analyse Num\u00e9rique"},{"issue":"1","key":"351_CR6","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1007\/s002110050228","volume":"75","author":"GM Crandall","year":"1996","unstructured":"Crandall, G.M., Lions, P.-L.: Convergent difference schemes for nonlinear parabolic equations and mean curvature motion. Numerische Mathematik 75(1), 17\u201341 (1996)","journal-title":"Numerische Mathematik"},{"issue":"1","key":"351_CR7","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1090\/S0273-0979-1992-00266-5","volume":"27","author":"MG Crandall","year":"1992","unstructured":"Crandall, M.G., Ishii, H., Lions, P.-L.: User\u2019s guide to viscosity solutions of second order partial differential equations. Bull. Am. Math. Soc. 27(1), 1\u201367 (1992)","journal-title":"Bull. Am. Math. Soc."},{"issue":"2","key":"351_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\u2013+an unsymmetric-pattern multifrontal method. ACM Trans. Math. Softw. 30(2), 196\u2013199 (2004)","journal-title":"ACM Trans. Math. Softw."},{"issue":"283","key":"351_CR9","doi-asserted-by":"crossref","first-page":"1433","DOI":"10.1090\/S0025-5718-2012-02632-9","volume":"82","author":"K Debrabant","year":"2013","unstructured":"Debrabant, K., Jakobsen, E.R.: Semi-Lagrangian schemes for linear and fully non-linear diffusion equations. Math. Comput. 82(283), 1433\u20131462 (2013)","journal-title":"Math. Comput."},{"issue":"2","key":"351_CR10","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1137\/0720023","volume":"20","author":"SC Eisenstat","year":"1983","unstructured":"Eisenstat, S.C., Elman, H.C., Schultz, M.H.: Variational iterative methods for nonsymmetric systems of linear equations. SIAM J. Numer. Anal. 20(2), 345\u2013357 (1983)","journal-title":"SIAM J. Numer. Anal."},{"issue":"2","key":"351_CR11","doi-asserted-by":"crossref","first-page":"1","DOI":"10.21314\/JCF.2007.163","volume":"11","author":"PA Forsyth","year":"2007","unstructured":"Forsyth, P.A., Labahn, G.: Numerical methods for controlled Hamilton\u2013Jacobi\u2013Bellman PDEs in finance. J. Comput. Finance 11(2), 1 (2007)","journal-title":"J. Comput. Finance"},{"key":"351_CR12","doi-asserted-by":"crossref","first-page":"503","DOI":"10.1007\/978-3-642-17254-0_18","volume-title":"Handbook of computational finance. Springer Handbooks of Computational Statistics","author":"PA Forsyth","year":"2012","unstructured":"Forsyth, P.A., Vetzal, K.R.: Numerical methods for nonlinear PDEs in finance. In: Duan, J.-C., H\u00e4rdle, W.K., Gentle, J.E. (eds.) Handbook of computational finance. Springer Handbooks of Computational Statistics, pp. 503\u2013528. Springer, Berlin (2012)"},{"issue":"5","key":"351_CR13","doi-asserted-by":"crossref","first-page":"S323","DOI":"10.1137\/120881476","volume":"35","author":"D Han","year":"2013","unstructured":"Han, D., Wan, J.W.L.: Multigrid methods for second order Hamilton\u2013Jacobi\u2013Bellman and Hamilton\u2013Jacobi\u2013Bellman\u2013Isaacs equations. SIAM J. Sci. Comput. 35(5), S323\u2013S344 (2013)","journal-title":"SIAM J. Sci. Comput."},{"issue":"2\u20133","key":"351_CR14","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1007\/BF01389627","volume":"49","author":"R Hoppe","year":"1986","unstructured":"Hoppe, R.: Multi-grid methods for Hamilton\u2013Jacobi\u2013Bellman equations. Numerische Mathematik 49(2\u20133), 239\u2013254 (1986)","journal-title":"Numerische Mathematik"},{"key":"351_CR15","unstructured":"HSL: A collection of Fortran codes for large scale scientific computation. http:\/\/www.hsl.rl.ac.uk\/ (2015)"},{"issue":"1\u20132","key":"351_CR16","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1002\/nla.317","volume":"10","author":"H Kim","year":"2003","unstructured":"Kim, H., Xu, J., Zikatanov, L.: A multigrid method based on graph matching for convection-diffusion equations. Numer. Linear Algebra Appl. 10(1\u20132), 181\u2013195 (2003)","journal-title":"Numer. Linear Algebra Appl."},{"key":"351_CR17","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4613-0007-6","volume-title":"Numerical Methods for Stochastic Control Problems in Continuous Time","author":"HJ Kushner","year":"2001","unstructured":"Kushner, H.J., Dupuis, P.: Numerical Methods for Stochastic Control Problems in Continuous Time, vol. 24. Springer, Berlin (2001)"},{"issue":"11","key":"351_CR18","doi-asserted-by":"crossref","first-page":"1229","DOI":"10.1080\/03605308308820301","volume":"8","author":"P-L Lions","year":"1983","unstructured":"Lions, P.-L.: Optimal control of diffusion processes and Hamilton\u2013Jacobi\u2013Bellman equations part 2: viscosity solutions and uniqueness. Commun. Partial Differ. Eq. 8(11), 1229\u20131276 (1983)","journal-title":"Commun. Partial Differ. Eq."},{"key":"351_CR19","doi-asserted-by":"publisher","unstructured":"Ma, K., Forsyth, P.A.: An unconditionally monotone numerical scheme for the two factor uncertain volatility model. IMA J. Numer. Anal. (2016). doi: 10.1093\/imanum\/drw025","DOI":"10.1093\/imanum\/drw025"},{"issue":"3","key":"351_CR20","doi-asserted-by":"crossref","first-page":"579","DOI":"10.1137\/0327031","volume":"27","author":"J-L Menaldi","year":"1989","unstructured":"Menaldi, J.-L.: Some estimates for finite difference approximations. SIAM J. Control Optim. 27(3), 579\u2013607 (1989)","journal-title":"SIAM J. Control Optim."},{"issue":"1","key":"351_CR21","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1002\/sapm1952311253","volume":"31","author":"TS Motzkin","year":"1952","unstructured":"Motzkin, T.S., Wasow, W.: On the approximation of linear elliptic differential equations by difference equations with positive coefficients. J. Math. Phys. 31(1), 253\u2013259 (1952)","journal-title":"J. Math. Phys."},{"issue":"2","key":"351_CR22","doi-asserted-by":"crossref","first-page":"A1079","DOI":"10.1137\/100818509","volume":"34","author":"A Napov","year":"2012","unstructured":"Napov, A., Notay, Y.: An algebraic multigrid method with guaranteed convergence rate. SIAM J. Sci. Comput. 34(2), A1079\u2013A1109 (2012)","journal-title":"SIAM J. Sci. Comput."},{"key":"351_CR23","unstructured":"Notay, Y.: Homepage for AGMG. http:\/\/homepages.ulb.ac.be\/~ynotay\/AGMG\/"},{"issue":"6","key":"351_CR24","first-page":"123","volume":"37","author":"Y Notay","year":"2010","unstructured":"Notay, Y.: An aggregation-based algebraic multigrid method. Electron. Trans. Numer. Anal. 37(6), 123\u2013146 (2010)","journal-title":"Electron. Trans. Numer. Anal."},{"issue":"4","key":"351_CR25","doi-asserted-by":"crossref","first-page":"A2288","DOI":"10.1137\/110835347","volume":"34","author":"Y Notay","year":"2012","unstructured":"Notay, Y.: Aggregation-based algebraic multigrid for convection-diffusion equations. SIAM J. Sci. Comput. 34(4), A2288\u2013A2316 (2012)","journal-title":"SIAM J. Sci. Comput."},{"issue":"5","key":"351_CR26","doi-asserted-by":"crossref","first-page":"473","DOI":"10.1002\/nla.542","volume":"15","author":"Y Notay","year":"2008","unstructured":"Notay, Y., Vassilevski, P.S.: Recursive Krylov-based multigrid cycles. Numer. Linear Algebra Appl. 15(5), 473\u2013487 (2008)","journal-title":"Numer. Linear Algebra Appl."},{"issue":"2","key":"351_CR27","doi-asserted-by":"crossref","first-page":"879","DOI":"10.1137\/S0036142903435235","volume":"44","author":"AM Oberman","year":"2006","unstructured":"Oberman, A.M.: Convergent difference schemes for degenerate elliptic and parabolic equations: Hamilton\u2013Jacobi equations and free boundary problems. SIAM J. Numer. Anal. 44(2), 879\u2013895 (2006)","journal-title":"SIAM J. Numer. Anal."},{"key":"351_CR28","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1137\/1.9781611971057.ch4","volume":"3","author":"J Ruge","year":"1987","unstructured":"Ruge, J., St\u00fcben, K.: Algebraic multigrid. Multigrid Methods 3, 73\u2013130 (1987)","journal-title":"Multigrid Methods"},{"key":"351_CR29","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898718003","volume-title":"Iterative Methods for Sparse Linear Systems","author":"Y Saad","year":"2003","unstructured":"Saad, Y.: Iterative Methods for Sparse Linear Systems, 2nd edn. Society for Industrial and Applied Mathematics, Philadelphia (2003)","edition":"2"},{"issue":"3","key":"351_CR30","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(3), 856\u2013869 (1986)","journal-title":"SIAM J. Sci. Stat. Comput."},{"key":"351_CR31","doi-asserted-by":"crossref","unstructured":"St\u00fcben, K.: A review of algebraic multigrid. J. Comput. Appl. Math., 128(1-2), 281\u2013309, 2001. Numerical Analysis 2000. Vol. VII: Partial Differential Equations","DOI":"10.1016\/B978-0-444-50616-0.50012-9"},{"key":"351_CR32","volume-title":"Multigrid","author":"U Trottenberg","year":"2001","unstructured":"Trottenberg, U., Oosterlee, C., Sch\u00fcller, A.: Multigrid. Academic Press, Cambridge (2001)"},{"issue":"2","key":"351_CR33","doi-asserted-by":"crossref","first-page":"631","DOI":"10.1137\/0913035","volume":"13","author":"HA Vorst van der","year":"1992","unstructured":"van der Vorst, H.A.: Bi-CGSTAB: a fast and smoothly converging variant of Bi\u2013CG for the solution of nonsymmetric linear systems. SIAM J. Sci. Stat. Comput. 13(2), 631\u2013644 (1992)","journal-title":"SIAM J. Sci. Stat. Comput."},{"key":"351_CR34","volume-title":"Multilevel Block Factorization Preconditioners: Matrix-Based Analysis and Algorithms for Solving Finite Element Equations","author":"PS Vassilevski","year":"2008","unstructured":"Vassilevski, P.S.: Multilevel Block Factorization Preconditioners: Matrix-Based Analysis and Algorithms for Solving Finite Element Equations. Springer, Berlin (2008)"},{"key":"351_CR35","doi-asserted-by":"crossref","first-page":"1122","DOI":"10.1007\/s10915-015-0057-9","volume":"66","author":"X Warin","year":"2013","unstructured":"Warin, X.: Some non-monotone schemes for time dependent Hamilton-Jacobi-Bellman equations in stochastic control. J. Sci. Comput. 66, 1122\u20131147 (2013)","journal-title":"J. Sci. Comput."},{"key":"351_CR36","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1017\/S0962492915000021","volume":"24","author":"AJ Wathen","year":"2015","unstructured":"Wathen, A.J.: Preconditioning. Acta Numer. 24, 329\u2013376 (2015)","journal-title":"Acta Numer."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10915-016-0351-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-016-0351-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-016-0351-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,9,28]],"date-time":"2020-09-28T23:43:39Z","timestamp":1601336619000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-016-0351-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,1,13]]},"references-count":36,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2017,7]]}},"alternative-id":["351"],"URL":"https:\/\/doi.org\/10.1007\/s10915-016-0351-1","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,1,13]]}}}