{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T00:48:27Z","timestamp":1740098907176,"version":"3.37.3"},"publisher-location":"Cham","reference-count":38,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319623917"},{"type":"electronic","value":"9783319623924"}],"license":[{"start":{"date-parts":[[2017,1,1]],"date-time":"2017-01-01T00:00:00Z","timestamp":1483228800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2017]]},"DOI":"10.1007\/978-3-319-62392-4_1","type":"book-chapter","created":{"date-parts":[[2017,7,4]],"date-time":"2017-07-04T22:34:09Z","timestamp":1499207649000},"page":"3-19","source":"Crossref","is-referenced-by-count":1,"title":["An Analysis of Reordering Algorithms to Reduce the Computational Cost of the Jacobi-Preconditioned CG Solver Using High-Precision Arithmetic"],"prefix":"10.1007","author":[{"given":"Sanderson L.","family":"Gonzaga de Oliveira","sequence":"first","affiliation":[]},{"given":"Guilherme Oliveira","family":"Chagas","sequence":"additional","affiliation":[]},{"given":"J\u00fanior Assis Barreto","family":"Bernardes","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2017,7,6]]},"reference":[{"issue":"3","key":"1_CR1","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1109\/MCSE.2005.52","volume":"7","author":"DH Bailey","year":"2005","unstructured":"Bailey, D.H.: High-precision floating-point arithmetic in scientific computation. Comput. Sci. Eng. 7(3), 54\u201361 (2005)","journal-title":"Comput. Sci. Eng."},{"key":"1_CR2","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1016\/j.procs.2015.05.231","volume":"51","author":"JAB Bernardes","year":"2015","unstructured":"Bernardes, J.A.B., Gonzaga de Oliveira, S.L.: A systematic review of heuristics for profile reduction of symmetric matrices. Procedia Comput. Sci. 51, 221\u2013230 (2015). (International Conference on Computational Science, ICCS)","journal-title":"Procedia Comput. Sci."},{"issue":"3","key":"1_CR3","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1016\/S0965-9978(96)00039-7","volume":"28","author":"DA Burgess","year":"1997","unstructured":"Burgess, D.A., Giles, M.: Renumbering unstructured grids to improve the performance of codes on hierarchial memory machines. Adv. Eng. Softw. 28(3), 189\u2013201 (1997)","journal-title":"Adv. Eng. Softw."},{"key":"1_CR4","doi-asserted-by":"crossref","first-page":"1693","DOI":"10.1002\/nme.1620230909","volume":"23","author":"IW Burgess","year":"1986","unstructured":"Burgess, I.W., Lai, P.K.F.: A new node renumbering algorithm for bandwidth reduction. Int. J. Numer. Methods Eng. 23, 1693\u20131704 (1986)","journal-title":"Int. J. Numer. Methods Eng."},{"key":"1_CR5","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1016\/j.procs.2015.05.229","volume":"51","author":"GO Chagas","year":"2015","unstructured":"Chagas, G.O., Gonzaga de Oliveira, S.L.: Metaheuristic-based heuristics for symmetric-matrix bandwidth reduction: a systematic review. Procedia Comput. Sci. (ICCS) 51, 211\u2013220 (2015)","journal-title":"Procedia Comput. Sci. (ICCS)"},{"issue":"3","key":"1_CR6","doi-asserted-by":"crossref","first-page":"489","DOI":"10.2514\/3.12012","volume":"32","author":"R Das","year":"1994","unstructured":"Das, R., Mavriplis, D.J., Saltz, J.H., Gupta, S.K., Ponnusamy, R.: Design and implementation of a parallel unstructured Euler solver using software primitives. AIAA J. 32(3), 489\u2013496 (1994)","journal-title":"AIAA J."},{"issue":"1","key":"1_CR7","first-page":"1:1","volume":"38","author":"TA Davis","year":"2011","unstructured":"Davis, T.A., Hu, Y.: The University of Florida sparse matrix collection. ACM Trans. Math. Softw. 38(1), 1:1\u20131:25 (2011)","journal-title":"ACM Trans. Math. Softw."},{"issue":"4","key":"1_CR8","doi-asserted-by":"crossref","first-page":"635","DOI":"10.1007\/BF01932738","volume":"29","author":"IS Duff","year":"1989","unstructured":"Duff, I.S., Meurant, G.A.: The effect of ordering on preconditioned conjugate gradients. BIT Numer. Math. 29(4), 635\u2013657 (1989)","journal-title":"BIT Numer. Math."},{"issue":"1","key":"1_CR9","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1016\/0045-7949(75)90016-4","volume":"5","author":"CA Felippa","year":"1975","unstructured":"Felippa, C.A.: Solution of linear equations with skyline-stored symmetric matrix. Comput. Struct. 5(1), 13\u201329 (1975)","journal-title":"Comput. Struct."},{"key":"1_CR10","volume-title":"Computer Solution of Large Sparse Positive Definite Systems","author":"A George","year":"1981","unstructured":"George, A., Liu, J.W.: Computer Solution of Large Sparse Positive Definite Systems. Prentice-Hall, Englewood Cliffs (1981)"},{"issue":"3","key":"1_CR11","doi-asserted-by":"crossref","first-page":"284","DOI":"10.1145\/355841.355845","volume":"5","author":"A George","year":"1979","unstructured":"George, A., Liu, J.W.H.: An implementation of a pseudoperipheral node finder. ACM Trans. Math. Softw. 5(3), 284\u2013295 (1979)","journal-title":"ACM Trans. Math. Softw."},{"issue":"2","key":"1_CR12","doi-asserted-by":"crossref","first-page":"236","DOI":"10.1137\/0713023","volume":"13","author":"NE Gibbs","year":"1976","unstructured":"Gibbs, N.E., Poole, 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."},{"key":"1_CR13","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"54","DOI":"10.1007\/978-3-319-42085-1_5","volume-title":"Computational Science and Its Applications \u2013 ICCSA 2016","author":"SL Gonzaga de Oliveira","year":"2016","unstructured":"Gonzaga de Oliveira, S.L., Abreu, A.A.A.M., Robaina, D., Kischinhevsky, M.: A new heuristic for bandwidth and profile reductions of matrices using a self-organizing map. In: Gervasi, O., et al. (eds.) ICCSA 2016. LNCS, vol. 9786, pp. 54\u201370. Springer, Cham (2016). doi: 10.1007\/978-3-319-42085-1_5"},{"issue":"2","key":"1_CR14","doi-asserted-by":"crossref","first-page":"190","DOI":"10.1504\/IJBIDM.2017.084281","volume":"12","author":"SL Gonzaga de Oliveira","year":"2017","unstructured":"Gonzaga de Oliveira, S.L., Abreu, A.A.A.M., Robaina, D.T., Kischnhevsky, M.: An evaluation of four reordering algorithms to reduce the computational cost of the Jacobi-preconditioned conjugate gradient method using high-precision arithmetic. Int. J. Bus. Intell. Data Min. 12(2), 190\u2013209 (2017). http:\/\/dx.doi.org\/10.1504\/IJBIDM.2017.10004158","journal-title":"Int. J. Bus. Intell. Data Min."},{"key":"1_CR15","doi-asserted-by":"publisher","unstructured":"Gonzaga de Oliveira, S.L., Bernardes, J.A.B., Chagas, G.O.: An evaluation of low-cost heuristics for matrix bandwidth and profile reductions. Comput. Appl. Math. (2016). doi: 10.1007\/s40314-016-0394-9","DOI":"10.1007\/s40314-016-0394-9"},{"key":"1_CR16","doi-asserted-by":"crossref","unstructured":"Gonzaga de Oliveira, S.L., Bernardes, J.A.B., Chagas, G.O.: An evaluation of several heuristics for bandwidth and profile reductions to reduce the computational cost of the preconditioned conjugate gradient method. In: The XLVIII of the Brazilian Symposium of Operations Research (SBPO), Vit\u00f3ria, Brazil, September 2016","DOI":"10.1007\/s40314-016-0394-9"},{"key":"1_CR17","unstructured":"Gonzaga de Oliveira, S.L., Chagas, G.O.: A systematic review of heuristics for symmetric-matrix bandwidth reduction: methods not based on metaheuristics. In: The XLVII Brazilian Symposium of Operational Research (SBPO), Ipojuca-PE, Brazil, August 2015. Sobrapo"},{"key":"1_CR18","unstructured":"Gonzaga de Oliveira, S.L., Kischinhevsky, M.: Sierpi\u0144ski curve for total ordering of a graph-based adaptive simplicial-mesh refinement for finite volume discretizations. In: Proceedings of the Brazilian National Conference on Computational and Applied Mathematics (CNMAC), pp. 581\u2013585, Bel\u00e9m, Brazil (2008)"},{"issue":"2","key":"1_CR19","first-page":"119","volume":"95","author":"SL Gonzaga de Oliveira","year":"2013","unstructured":"Gonzaga de Oliveira, S.L., Kischinhevsky, M., Tavares, J.M.R.S.: Novel graph-based adaptive triangular mesh refinement for finite-volume discretizations. Comput. Model. Eng. Sci. 95(2), 119\u2013141 (2013)","journal-title":"Comput. Model. Eng. Sci."},{"key":"1_CR20","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"502","DOI":"10.1007\/978-3-319-21404-7_37","volume-title":"Computational Science and Its Applications \u2013 ICCSA 2015","author":"SL Gonzaga de Oliveira","year":"2015","unstructured":"Gonzaga de Oliveira, S.L., Oliveira, F.S., Chagas, G.O.: A novel approach to the weighted laplacian formulation applied to 2D delaunay triangulations. In: Gervasi, O., Murgante, B., Misra, S., Gavrilova, M.L., Rocha, A.M.A.C., Torre, C., Taniar, D., Apduhan, B.O. (eds.) ICCSA 2015. LNCS, vol. 9155, pp. 502\u2013515. Springer, Cham (2015). doi: 10.1007\/978-3-319-21404-7_37"},{"issue":"36","key":"1_CR21","doi-asserted-by":"crossref","first-page":"409","DOI":"10.6028\/jres.049.044","volume":"49","author":"MR Hestenes","year":"1952","unstructured":"Hestenes, M.R., Stiefel, E.: Methods of conjugate gradients for solving linear systems. J. Res. Natl. Bur. Stand. 49(36), 409\u2013436 (1952)","journal-title":"J. Res. Natl. Bur. Stand."},{"key":"1_CR22","doi-asserted-by":"crossref","unstructured":"Johnson, D.: A theoretician\u2019s guide to the experimental analysis of algorithms. In: Goldwasser, M., Johnson, D.S., McGeoch, C.C., (eds.) Proceedings of the 5th and 6th DIMACS Implementation Challenges, Providence (2002)","DOI":"10.1090\/dimacs\/059\/11"},{"issue":"2","key":"1_CR23","first-page":"39","volume":"36","author":"A Kaveh","year":"2012","unstructured":"Kaveh, A., Sharafi, P.: Ordering for bandwidth and profile minimization problems via charged system search algorithm. IJST-T Civ. Eng. 36(2), 39\u201352 (2012)","journal-title":"IJST-T Civ. Eng."},{"key":"1_CR24","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1007\/978-1-4471-2318-7_7","volume-title":"Research and Development in Intelligent Systems XXVIII","author":"B Koohestani","year":"2011","unstructured":"Koohestani, B., Poli, R.: A hyper-heuristic approach to evolving algorithms for bandwidth reduction based on genetic programming. In: Bramer, M., Petridis, M., Nolle, L. (eds.) Research and Development in Intelligent Systems XXVIII, pp. 93\u2013106. Springer, London (2011). doi: 10.1007\/978-1-4471-2318-7_7"},{"issue":"3","key":"1_CR25","doi-asserted-by":"crossref","first-page":"559","DOI":"10.1007\/BF02510240","volume":"37","author":"G Kumfert","year":"1997","unstructured":"Kumfert, G., Pothen, A.: Two improved algorithms for envelope and wavefront reduction. BIT Numer. Math. 37(3), 559\u2013590 (1997)","journal-title":"BIT Numer. Math."},{"issue":"1","key":"1_CR26","doi-asserted-by":"crossref","first-page":"33","DOI":"10.6028\/jres.049.006","volume":"49","author":"C Lanczos","year":"1952","unstructured":"Lanczos, C.: Solutions of systems of linear equations by minimized iterations. J. Res. Natl. Bur. Stand. 49(1), 33\u201353 (1952)","journal-title":"J. Res. Natl. Bur. Stand."},{"key":"1_CR27","doi-asserted-by":"crossref","first-page":"537","DOI":"10.1142\/S0218213007003394","volume":"3","author":"A Lim","year":"2007","unstructured":"Lim, A., Rodrigues, B., Xiao, F.: A fast algorithm for bandwidth minimization. Int. J. Artif. Intell. Tools 3, 537\u2013544 (2007)","journal-title":"Int. J. Artif. Intell. Tools"},{"issue":"1","key":"1_CR28","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1007\/BF02006264","volume":"10","author":"YX Lin","year":"1994","unstructured":"Lin, Y.X., Yuan, J.J.: Profile minimization problem for matrices and graphs. Acta Mathematicae Applicatae Sinica 10(1), 107\u2013122 (1994)","journal-title":"Acta Mathematicae Applicatae Sinica"},{"issue":"3","key":"1_CR29","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1108\/eb023906","volume":"10","author":"SRP Medeiros","year":"1993","unstructured":"Medeiros, S.R.P., Pimenta, P.M., Goldenberg, P.: Algorithm for profile and wavefront reduction of sparse matrices with a symmetric structure. Eng. Comput. 10(3), 257\u2013266 (1993)","journal-title":"Eng. Comput."},{"key":"1_CR30","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1016\/j.ejor.2008.12.015","volume":"200","author":"N Mladenovic","year":"2010","unstructured":"Mladenovic, N., Urosevic, D., P\u00e9rez-Brito, D., Garc\u00eda-Gonz\u00e1lez, C.G.: Variable neighbourhood search for bandwidth reduction. Eur. J. Oper. Res. 200, 14\u201327 (2010)","journal-title":"Eur. J. Oper. Res."},{"key":"1_CR31","first-page":"177","volume":"16","author":"CH Papadimitriou","year":"1976","unstructured":"Papadimitriou, C.H.: The NP-completeness of bandwidth minimization problem. Comput. J. 16, 177\u2013192 (1976)","journal-title":"Comput. J."},{"issue":"12","key":"1_CR32","doi-asserted-by":"crossref","first-page":"1737","DOI":"10.1002\/(SICI)1097-0207(19990830)45:12<1737::AID-NME652>3.0.CO;2-T","volume":"45","author":"JK Reid","year":"1999","unstructured":"Reid, J.K., Scott, J.A.: Ordering symmetric sparse matrices for small profile and wavefront. Int. J. Numer. Methods Eng. 45(12), 1737\u20131755 (1999)","journal-title":"Int. J. Numer. Methods Eng."},{"key":"1_CR33","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. Comput. 7, 856\u2013869 (1986)","journal-title":"SIAM J. Sci. Comput."},{"issue":"11","key":"1_CR34","doi-asserted-by":"crossref","first-page":"2651","DOI":"10.1002\/nme.1620281111","volume":"28","author":"SW Sloan","year":"1989","unstructured":"Sloan, S.W.: A Fortran program for profile and wavefront reduction. Int. J. Numer. Methods Eng. 28(11), 2651\u20132679 (1989)","journal-title":"Int. J. Numer. Methods Eng."},{"issue":"4","key":"1_CR35","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1007\/BF02521587","volume":"50","author":"RA Snay","year":"1976","unstructured":"Snay, R.A.: Reducing the profile of sparse symmetric matrices. Bulletin Geod\u00e9sique 50(4), 341\u2013352 (1976)","journal-title":"Bulletin Geod\u00e9sique"},{"key":"1_CR36","unstructured":"The MathWorks, Inc.: MATLAB, 1994\u20132015. http:\/\/www.mathworks.com\/products\/matlab"},{"issue":"1","key":"1_CR37","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1007\/s003710050160","volume":"15","author":"L Velho","year":"1999","unstructured":"Velho, L., Figueiredo, L.H., Gomes, J.: Hierarchical generalized triangle strips. Vis. Comput. 15(1), 21\u201335 (1999)","journal-title":"Vis. Comput."},{"key":"1_CR38","doi-asserted-by":"crossref","first-page":"121","DOI":"10.2528\/PIER09010512","volume":"90","author":"Q Wang","year":"2009","unstructured":"Wang, Q., Guo, Y.C., Shi, X.W.: A generalized GPS algorithm for reducing the bandwidth and profile of a sparse matrix. Prog. Electromagn. Res. 90, 121\u2013136 (2009)","journal-title":"Prog. Electromagn. Res."}],"container-title":["Lecture Notes in Computer Science","Computational Science and Its Applications \u2013 ICCSA 2017"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-62392-4_1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,28]],"date-time":"2019-09-28T09:24:57Z","timestamp":1569662697000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-319-62392-4_1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017]]},"ISBN":["9783319623917","9783319623924"],"references-count":38,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-62392-4_1","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2017]]}}}