{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,25]],"date-time":"2025-03-25T19:39:01Z","timestamp":1742931541389,"version":"3.40.3"},"publisher-location":"Cham","reference-count":84,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783030479558"},{"type":"electronic","value":"9783030479565"}],"license":[{"start":{"date-parts":[[2020,1,1]],"date-time":"2020-01-01T00:00:00Z","timestamp":1577836800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2020,7,31]],"date-time":"2020-07-31T00:00:00Z","timestamp":1596153600000},"content-version":"vor","delay-in-days":212,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020]]},"DOI":"10.1007\/978-3-030-47956-5_7","type":"book-chapter","created":{"date-parts":[[2020,7,30]],"date-time":"2020-07-30T17:26:56Z","timestamp":1596130016000},"page":"143-187","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["ESSEX: Equipping Sparse Solvers For Exascale"],"prefix":"10.1007","author":[{"given":"Christie L.","family":"Alappat","sequence":"first","affiliation":[]},{"given":"Andreas","family":"Alvermann","sequence":"additional","affiliation":[]},{"given":"Achim","family":"Basermann","sequence":"additional","affiliation":[]},{"given":"Holger","family":"Fehske","sequence":"additional","affiliation":[]},{"given":"Yasunori","family":"Futamura","sequence":"additional","affiliation":[]},{"given":"Martin","family":"Galgon","sequence":"additional","affiliation":[]},{"given":"Georg","family":"Hager","sequence":"additional","affiliation":[]},{"given":"Sarah","family":"Huber","sequence":"additional","affiliation":[]},{"given":"Akira","family":"Imakura","sequence":"additional","affiliation":[]},{"given":"Masatoshi","family":"Kawai","sequence":"additional","affiliation":[]},{"given":"Moritz","family":"Kreutzer","sequence":"additional","affiliation":[]},{"given":"Bruno","family":"Lang","sequence":"additional","affiliation":[]},{"given":"Kengo","family":"Nakajima","sequence":"additional","affiliation":[]},{"given":"Melven","family":"R\u00f6hrig-Z\u00f6llner","sequence":"additional","affiliation":[]},{"given":"Tetsuya","family":"Sakurai","sequence":"additional","affiliation":[]},{"given":"Faisal","family":"Shahzad","sequence":"additional","affiliation":[]},{"given":"Jonas","family":"Thies","sequence":"additional","affiliation":[]},{"given":"Gerhard","family":"Wellein","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,7,31]]},"reference":[{"key":"7_CR1","unstructured":"Alappat, C.L., Hager, G., Schenk, O., Thies, J., Basermann, A., Bishop, A.R., Fehske, H., Wellein, G.: A recursive algebraic coloring technique for hardware-efficient symmetric sparse matrix-vector multiplication. Accepted for publication in ACM Transactions on Parallel Computing. Preprint: http:\/\/arxiv.org\/abs\/1907.06487"},{"key":"7_CR2","doi-asserted-by":"crossref","unstructured":"Alvermann, A., Fehske, H.: Exciton mass and exciton spectrum in the cuprous oxide. J. Phys. B 51(4), 044001 (2018). https:\/\/doi.org\/10.1088\/1361-6455\/aaa060 . http:\/\/stacks.iop.org\/0953-4075\/51\/i=4\/a=044001","DOI":"10.1088\/1361-6455\/aaa060"},{"key":"7_CR3","doi-asserted-by":"crossref","first-page":"577","DOI":"10.1007\/978-3-319-14313-2_49","volume-title":"Euro-Par 2014: Parallel Processing Workshops. Lecture Notes in Computer Science","author":"A Alvermann","year":"2014","unstructured":"Alvermann, A., Basermann, A., Fehske, H., Galgon, M., Hager, G., Kreutzer, M., Kr\u00e4mer, L., Lang, B., Pieper, A., R\u00f6hrig-Z\u00f6llner, M., Shahzad, F., Thies, J., Wellein, G.: ESSEX: equipping sparse solvers for exascale. In: Lopes, L. et al. (eds.) Euro-Par 2014: Parallel Processing Workshops. Lecture Notes in Computer Science, vol. 8806, pp. 577\u2013588. Springer, Berlin (2014). http:\/\/doi.org\/10.1007\/978-3-319-14313-2_49"},{"key":"7_CR4","doi-asserted-by":"crossref","unstructured":"Alvermann, A., Basermann, A., Bungartz, H.J., Carbogno, C., Ernst, D., Fehske, H., Futamura, Y., Galgon, M., Hager, G., Huber, S., Huckle, T., Ida, A., Imakura, A., Kawai, M., K\u00f6cher, S., Kreutzer, M., Kus, P., Lang, B., Lederer, H., Manin, V., Marek, A., Nakajima, K., Nemec, L., Reuter, K., Rippl, M., R\u00f6hrig-Z\u00f6llner, M., Sakurai, T., Scheffler, M., Scheurer, C., Shahzad, F., Simoes Brambila, D., Thies, J., Wellein, G.: Benefits from using mixed precision computations in the ELPA-AEO and ESSEX-II eigensolver projects. Jpn. J. Ind. Appl. Math. 36, 699\u2013717 (2019). https:\/\/doi.org\/10.1007\/s13160-019-00360-8","DOI":"10.1007\/s13160-019-00360-8"},{"key":"7_CR5","unstructured":"Anzt, H., Tomov, S., Dongarra, J.: Accelerating the LOBPCG method on GPUs using a blocked sparse matrix vector product. University of Tennessee Innovative Computing Laboratory Technical Report UT-EECS-14-731 (2014). http:\/\/www.eecs.utk.edu\/resources\/library\/589"},{"key":"7_CR6","unstructured":"Anzt, H., Tomov, S., Dongarra, J.: Implementing a sparse matrix vector product for the SELL-C\/SELL-C-\u03c3 formats on NVIDIA GPUs. University of Tennessee Innovative Computing Laboratory Technical Report UT-EECS-14-727 (2014). http:\/\/www.eecs.utk.edu\/resources\/library\/585"},{"key":"7_CR7","doi-asserted-by":"publisher","first-page":"52","DOI":"10.14495\/jsiaml.1.52","volume":"1","author":"J Asakura","year":"2009","unstructured":"Asakura, J., Sakurai, T., Tadano, H., Ikegami, T., Kimura, K.: A numerical method for nonlinear eigenvalue problems using contour integrals. JSIAM Lett. 1, 52\u201355 (2009). https:\/\/doi.org\/10.14495\/jsiaml.1.52","journal-title":"JSIAM Lett."},{"issue":"1","key":"7_CR8","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1007\/s13160-010-0005-x","volume":"27","author":"J Asakura","year":"2010","unstructured":"Asakura, J., Sakurai, T., Tadano, H., Ikegami, T., Kimura, K.: A numerical method for polynomial eigenvalue problems using contour integral. Jpn. J. Ind. Appl. Math. 27(1), 73\u201390 (2010). https:\/\/doi.org\/10.1007\/s13160-010-0005-x","journal-title":"Jpn. J. Ind. Appl. Math."},{"key":"7_CR9","unstructured":"Balay, S., Abhyankar, S., Adams, M.F., Brown, J., Brune, P., Buschelman, K., Dalcin, L., Dener, A., Eijkhout, V., Gropp, W.D., Karpeyev, D., Kaushik, D., Knepley, M.G., May, D.A., McInnes, L.C., Mills, R.T., Munson, T., Rupp, K., Sanan, P., Smith, B.F., Zampini, S., Zhang, H., Zhang, H.: PETSc Web page (2019). https:\/\/www.mcs.anl.gov\/petsc"},{"key":"7_CR10","doi-asserted-by":"crossref","first-page":"526","DOI":"10.1016\/j.cam.2015.07.012","volume":"292","author":"MV Barel","year":"2016","unstructured":"Barel, M.V., Kravanja, P.: Nonlinear eigenvalue problems and contour integrals. J. Comput. Appl. Math. 292, 526\u2013540 (2016). https:\/\/doi.org\/10.1016\/j.cam.2015.07.012","journal-title":"J. Comput. Appl. Math."},{"issue":"1","key":"7_CR11","doi-asserted-by":"publisher","first-page":"69","DOI":"10.14529\/jsfi170104","volume":"4","author":"R Bartlett","year":"2017","unstructured":"Bartlett, R., Demeshko, I., Gamblin, T., Hammond, G., Heroux, M., Johnson, J., Klinvex, A., Li, X., McInnes, L., Moulton, J.D., Osei-Kuffuor, D., Sarich, J., Smith, B., Willenbring, J., Yang, U.M.: xSDK foundations: toward an extreme-scale scientific software development kit. Supercomput. Front. Innov. Int. J. 4(1), 69\u201382 (2017). https:\/\/doi.org\/10.14529\/jsfi170104","journal-title":"Supercomput. Front. Innov. Int. J."},{"key":"7_CR12","doi-asserted-by":"crossref","unstructured":"Beyn, W.J.: An integral method for solving nonlinear eigenvalue problems. Linear Algebra Appl. 436(10), 3839\u20133863 (2012). https:\/\/doi.org\/10.1016\/j.laa.2011.03.030 . Special Issue dedicated to Heinrich Voss\u2019s 65th birthday","DOI":"10.1016\/j.laa.2011.03.030"},{"key":"7_CR13","doi-asserted-by":"publisher","first-page":"109","DOI":"10.1103\/RevModPhys.81.109","volume":"81","author":"AH Castro Neto","year":"2009","unstructured":"Castro Neto, A.H., Guinea, F., Peres, N.M.R., Novoselov, K.S., Geim, A.K.: The electronic properties of graphene. Rev. Mod. Phys. 81, 109\u2013162 (2009). https:\/\/doi.org\/10.1103\/RevModPhys.81.109","journal-title":"Rev. Mod. Phys."},{"key":"7_CR14","unstructured":"Chen, Y.C., Meil\u0103, M.: Selecting the independent coordinates of manifolds with large aspect ratios (2019, e-prints). arXiv:1907.01651."},{"issue":"4","key":"7_CR15","doi-asserted-by":"crossref","first-page":"357","DOI":"10.21136\/AM.2017.0016-17","volume":"62","author":"H Chen","year":"2017","unstructured":"Chen, H., Imakura, A., Sakurai, T.: Improving backward stability of Sakurai-Sugiura method with balancing technique in polynomial eigenvalue problem. Appl. Math. 62(4), 357\u2013375 (2017). https:\/\/doi.org\/10.21136\/AM.2017.0016-17","journal-title":"Appl. Math."},{"key":"7_CR16","doi-asserted-by":"publisher","first-page":"17","DOI":"10.14495\/jsiaml.9.17","volume":"9","author":"H Chen","year":"2017","unstructured":"Chen, H., Maeda, Y., Imakura, A., Sakurai, T., Tisseur, F.: Improving the numerical stability of the Sakurai-Sugiura method for quadratic eigenvalue problems. JSIAM Lett. 9, 17\u201320 (2017). https:\/\/doi.org\/10.14495\/jsiaml.9.17","journal-title":"JSIAM Lett."},{"key":"7_CR17","doi-asserted-by":"crossref","unstructured":"Davis, T.A., Hu, Y.: The University of Florida sparse matrix collection. ACM Trans. Math. Softw. 38(1), 1:1\u20131:25 (2011). https:\/\/doi.org\/10.1145\/2049662.2049663","DOI":"10.1145\/2049662.2049663"},{"key":"7_CR18","doi-asserted-by":"crossref","unstructured":"Druskin, V., Knizhnerman, L.: Two polynomial methods to compute functions of symmetric matrices. U.S.S.R. Comput. Maths. Math. Phys. 29(6), 112\u2013121 (1989). https:\/\/doi.org\/10.1016\/S0041-5553(89)80020-5","DOI":"10.1016\/S0041-5553(89)80020-5"},{"key":"7_CR19","doi-asserted-by":"crossref","unstructured":"Edwards, H.C., Trott, C.R., Sunderland, D.: Kokkos: enabling manycore performance portability through polymorphic memory access patterns. J. Parallel Distrib. Comput. 74(12), 3202\u20133216 (2014). https:\/\/doi.org\/10.1016\/j.jpdc.2014.07.003 . Domain-Specific Languages and High-Level Frameworks for High-Performance Computing","DOI":"10.1016\/j.jpdc.2014.07.003"},{"key":"7_CR20","doi-asserted-by":"crossref","unstructured":"Ernst, D., Hager, G., Thies, J., Wellein, G.: Performance engineering for a tall & skinny matrix multiplication kernel on GPUs. In: Proceedings PPAM\u201919: the 13h International Conference on Parallel Processing and Applied Mathematics, Bialystok, Poland, September 8\u201311, 2019. https:\/\/doi.org\/10.1007\/978-3-030-43229-4_43","DOI":"10.1007\/978-3-030-43229-4_43"},{"key":"7_CR21","unstructured":"EXASTEEL project website: www.numerik.uni-koeln.de\/14426.html"},{"key":"7_CR22","unstructured":"Fukasawa, T., Shahzad, F., Nakajima, K., Wellein, G.: pFEM-CRAFT: a library for application-level fault-resilience based on the CRAFT framework. In: Poster at the 2018 SIAM Conference on Parallel Processing for Scientific Computing (SIAM PP18), Tokyo (2018)"},{"issue":"1","key":"7_CR23","doi-asserted-by":"crossref","first-page":"821","DOI":"10.1002\/pamm.201410391","volume":"14","author":"M Galgon","year":"2014","unstructured":"Galgon, M., Kr\u00e4mer, L., Lang, B., Alvermann, A., Fehske, H., Pieper, A.: Improving robustness of the FEAST algorithm and solving eigenvalue problems from graphene nanoribbons. PAMM 14(1), 821\u2013822 (2014). http:\/\/doi.org\/10.1002\/pamm.201410391","journal-title":"PAMM"},{"key":"7_CR24","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1016\/j.parco.2015.06.005","volume":"49","author":"M Galgon","year":"2015","unstructured":"Galgon, M., Kr\u00e4mer, L., Thies, J., Basermann, A., Lang, B.: On the parallel iterative solution of linear systems arising in the FEAST algorithm for computing inner eigenvalues. Parallel Comput. 49, 153\u2013163 (2015)","journal-title":"Parallel Comput."},{"key":"7_CR25","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1007\/978-3-319-62426-6_5","volume-title":"Eigenvalue Problems: Algorithms, Software and Applications in Petascale Computing","author":"M Galgon","year":"2017","unstructured":"Galgon, M., Kr\u00e4mer, L., Lang, B., Alvermann, A., Fehske, H., Pieper, A., Hager, G., Kreutzer, M., Shahzad, F., Wellein, G., Basermann, A., R\u00f6hrig-Z\u00f6llner, M., Thies, J.: Improved coefficients for polynomial filtering in ESSEX. In: Sakurai, T., Zhang, S.L., Imamura, T., Yamamoto, Y., Kuramashi, Y., Hoshi, T. (eds.) Eigenvalue Problems: Algorithms, Software and Applications in Petascale Computing, pp. 63\u201379. Springer, Cham (2017). https:\/\/doi.org\/10.1007\/978-3-319-62426-6_5"},{"issue":"1","key":"7_CR26","doi-asserted-by":"crossref","DOI":"10.1002\/nla.2124","volume":"25","author":"M Galgon","year":"2018","unstructured":"Galgon, M., Kr\u00e4mer, L., Lang, B.: Improving projection-based eigensolvers via adaptive techniques. Numer. Linear Algebra Appl. 25(1), e2124 (2018). http:\/\/dx.doi.org\/10.1002\/nla.2124","journal-title":"Numer. Linear Algebra Appl."},{"key":"7_CR27","doi-asserted-by":"crossref","unstructured":"Gamblin, T., LeGendre, M.P., Collette, M.R., Lee, G.L., Moody, A., de Supinski, B.R., Futral, W.S.: The Spack package manager: bringing order to HPC software chaos (2015). LLNL-CONF-669890","DOI":"10.1145\/2807591.2807623"},{"key":"7_CR28","unstructured":"Giorgi, P., Vialla, B.: Generating optimized sparse matrix vector product over finite fields. In: Proceedings of ICMS 2014: Fourth International Congress on Mathematical Software, Seoul. Lecture Notes in Computer Science, vol. 8592, pp. 685\u2013690. Springer, Berlin (2014). http:\/\/www.lirmm.fr\/~giorgi\/icms2014-giovia.pdf"},{"key":"7_CR29","doi-asserted-by":"crossref","unstructured":"Gordon, D., Gordon, R.: CGMN revisited: robust and efficient solution of stiff linear systems derived from elliptic partial differential equations. ACM Trans. Math. Softw. 35(3), 18:1\u201318:27 (2008). https:\/\/doi.org\/10.1145\/1391989.1391991","DOI":"10.1145\/1391989.1391991"},{"issue":"4","key":"7_CR30","doi-asserted-by":"crossref","first-page":"A2100","DOI":"10.1137\/140980090","volume":"37","author":"S Guettel","year":"2015","unstructured":"Guettel, S., Polizzi, E., Tang, P., Viaud, G.: Zolotarev quadrature rules and load balancing for the FEAST eigensolver. SIAM J. Sci. Comput. 37(4), A2100\u2013A2122 (2015). https:\/\/doi.org\/10.1137\/140980090","journal-title":"SIAM J. Sci. Comput."},{"key":"7_CR31","doi-asserted-by":"publisher","first-page":"3045","DOI":"10.1103\/RevModPhys.82.3045","volume":"82","author":"MZ Hasan","year":"2010","unstructured":"Hasan, M.Z., Kane, C.L.: Colloquium: topological insulators. Rev. Mod. Phys. 82, 3045\u20133067 (2010). https:\/\/doi.org\/10.1103\/RevModPhys.82.3045","journal-title":"Rev. Mod. Phys."},{"key":"7_CR32","doi-asserted-by":"publisher","first-page":"1","DOI":"10.14495\/jsiaml.8.1","volume":"8","author":"T Hasegawa","year":"2016","unstructured":"Hasegawa, T., Imakura, A., Sakurai, T.: Recovering from accuracy deterioration in the contour integral-based eigensolver. JSIAM Lett. 8, 1\u20134 (2016). https:\/\/doi.org\/10.14495\/jsiaml.8.1","journal-title":"JSIAM Lett."},{"issue":"3","key":"7_CR33","doi-asserted-by":"crossref","first-page":"397","DOI":"10.1145\/1089014.1089021","volume":"31","author":"MA Heroux","year":"2005","unstructured":"Heroux, M.A., Bartlett, R.A., Howle, V.E., Hoekstra, R.J., Hu, J.J., Kolda, T.G., Lehoucq, R.B., Long, K.R., Pawlowski, R.P., Phipps, E.T., Salinger, A.G., Thornquist, H.K., Tuminaro, R.S., Willenbring, J.M., Williams, A., Stanley, K.S.: An overview of the Trilinos project. ACM Trans. Math. Softw. 31(3), 397\u2013423 (2005). http:\/\/doi.acm.org\/10.1145\/1089014.1089021","journal-title":"ACM Trans. Math. Softw."},{"issue":"1365","key":"7_CR34","doi-asserted-by":"publisher","first-page":"238","DOI":"10.1098\/rspa.1963.0204","volume":"276","author":"J Hubbard","year":"1963","unstructured":"Hubbard, J., Flowers, B.H.: Electron correlations in narrow energy bands. Proc. Roy. Soc. Lond. A 276(1365), 238\u2013257 (1963). https:\/\/doi.org\/10.1098\/rspa.1963.0204","journal-title":"Proc. Roy. Soc. Lond. A"},{"key":"7_CR35","unstructured":"Huber, S., Futamura, Y., Galgon, M., Imakura, A., Lang, B., Sakurai, T.: Flexible subspace iteration with moments for an effective contour-integration based eigensolver (2019, in preparation)"},{"issue":"3A","key":"7_CR36","doi-asserted-by":"crossref","first-page":"825","DOI":"10.11650\/twjm\/1500405869","volume":"14","author":"T Ikegami","year":"2010","unstructured":"Ikegami, T., Sakurai, T.: Contour integral eigensolver for non-hermitian systems: a Rayleigh-Ritz-type approach. Taiwan. J. Math. 14(3A), 825\u2013837 (2010). http:\/\/www.jstor.org\/stable\/43834819","journal-title":"Taiwan. J. Math."},{"issue":"8","key":"7_CR37","doi-asserted-by":"crossref","first-page":"1927","DOI":"10.1016\/j.cam.2009.09.029","volume":"233","author":"T Ikegami","year":"2010","unstructured":"Ikegami, T., Sakurai, T., Nagashima, U.: A filter diagonalization for generalized eigenvalue problems based on the Sakurai\u2013Sugiura projection method. J. Comput. Appl. Math. 233(8), 1927\u20131936 (2010). https:\/\/doi.org\/10.1016\/j.cam.2009.09.029","journal-title":"J. Comput. Appl. Math."},{"issue":"2","key":"7_CR38","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1007\/s11075-016-0241-5","volume":"75","author":"A Imakura","year":"2017","unstructured":"Imakura, A., Sakurai, T.: Block Krylov-type complex moment-based eigensolvers for solving generalized eigenvalue problems. Numer. Algorithms 75(2), 413\u2013433 (2017). https:\/\/doi.org\/10.1007\/s11075-016-0241-5","journal-title":"Numer. Algorithms"},{"key":"7_CR39","doi-asserted-by":"crossref","unstructured":"Imakura, A., Sakurai, T.: Block SS\u2013CAA: a complex moment-based parallel nonlinear eigensolver using the block communication-avoiding Arnoldi procedure. Parallel Comput. 74, 34\u201348 (2018). https:\/\/doi.org\/10.1016\/j.parco.2017.11.007 . Parallel Matrix Algorithms and Applications (PMAA\u201916)","DOI":"10.1016\/j.parco.2017.11.007"},{"key":"7_CR40","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1016\/j.aml.2014.02.007","volume":"32","author":"A Imakura","year":"2014","unstructured":"Imakura, A., Du, L., Sakurai, T.: A block Arnoldi-type contour integral spectral projection method for solving generalized eigenvalue problems. Appl. Math. Lett. 32, 22\u201327 (2014). https:\/\/doi.org\/10.1016\/j.aml.2014.02.007","journal-title":"Appl. Math. Lett."},{"issue":"1","key":"7_CR41","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1007\/s11075-015-9987-4","volume":"71","author":"A Imakura","year":"2016","unstructured":"Imakura, A., Du, L., Sakurai, T.: Error bounds of Rayleigh\u2013Ritz type contour integral-based eigensolver for solving generalized eigenvalue problems. Numer. Algorithms 71(1), 103\u2013120 (2016). https:\/\/doi.org\/10.1007\/s11075-015-9987-4","journal-title":"Numer. Algorithms"},{"issue":"3","key":"7_CR42","doi-asserted-by":"crossref","first-page":"721","DOI":"10.1007\/s13160-016-0224-x","volume":"33","author":"A Imakura","year":"2016","unstructured":"Imakura, A., Du, L., Sakurai, T.: Relationships among contour integral-based methods for solving generalized eigenvalue problems. Jpn. J. Ind. Appl. Math. 33(3), 721\u2013750 (2016). https:\/\/doi.org\/10.1007\/s13160-016-0224-x","journal-title":"Jpn. J. Ind. Appl. Math."},{"key":"7_CR43","first-page":"1","volume-title":"Eigenvalue Problems: Algorithms, Software and Applications in Petascale Computing","author":"A Imakura","year":"2017","unstructured":"Imakura, A., Futamura, Y., Sakurai, T.: An error resilience strategy of a complex moment-based eigensolver. In: Sakurai, T., Zhang, S.L., Imamura, T., Yamamoto, Y., Kuramashi, Y., Hoshi, T. (eds.) Eigenvalue Problems: Algorithms, Software and Applications in Petascale Computing, pp. 1\u201318. Springer, Cham (2017)"},{"key":"7_CR44","doi-asserted-by":"publisher","unstructured":"Iwashita, T., Nakashima, H., Takahashi, Y.: Algebraic block multi-color ordering method for parallel multi-threaded sparse triangular solver in ICCG method. In: Proceedings of the 2012 IEEE 26th International Parallel and Distributed Processing Symposium, IPDPS\u201912, pp. 474\u2013483. IEEE Computer Society, Washington (2012). https:\/\/doi.org\/10.1109\/IPDPS.2012.51","DOI":"10.1109\/IPDPS.2012.51"},{"key":"7_CR45","first-page":"292","volume":"2012","author":"M Kawai","year":"2013","unstructured":"Kawai, M., Iwashita, T., Nakashima, H., Marques, O.: Parallel smoother based on block red-black ordering for multigrid Poisson solver. In: High Performance Computing for Computational Science \u2013 VECPAR 2012, pp. 292\u2013299 (2013)","journal-title":"In: High Performance Computing for Computational Science \u2013 VECPAR"},{"key":"7_CR46","doi-asserted-by":"publisher","unstructured":"Kawai, M., Ida, A., Nakajima, K.: Hierarchical parallelization of multi-coloring algorithms for block IC preconditioners. In: 2017 IEEE 19th International Conference on High Performance Computing and Communications; IEEE 15th International Conference on Smart City; IEEE 3rd International Conference on Data Science and Systems (HPCC\/SmartCity\/DSS), pp. 138\u2013145. IEEE, Piscataway (2017). https:\/\/doi.org\/10.1109\/HPCC-SmartCity-DSS.2017.18","DOI":"10.1109\/HPCC-SmartCity-DSS.2017.18"},{"key":"7_CR47","unstructured":"Kawai, M., Ida, A., Nakajima, K.: Modified IC preconditioner of CG method for ill-conditioned problems (in Japanese). Tech. Rep. vol. 2017-HPC-158, No.9, IPSJ SIG (2017)"},{"key":"7_CR48","unstructured":"Kawai, M., Ida, A., Nakajima, K.: Higher precision for block ILU preconditioner. In: CoSaS2018. FAU (2018)"},{"key":"7_CR49","unstructured":"Kr\u00e4mer, L.: Integration based solvers for standard and generalized Hermitian eigenvalue problems. Ph.D. Thesis, Bergische Universit\u00e4t Wuppertal (2014). http:\/\/nbn-resolving.de\/urn\/resolver.pl?urn=urn:nbn:de:hbz:468-20140701-112141-6"},{"key":"7_CR50","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.cam.2012.11.014","volume":"244","author":"L Kr\u00e4mer","year":"2013","unstructured":"Kr\u00e4mer, L., Di Napoli, E., Galgon, M., Lang, B., Bientinesi, P.: Dissecting the FEAST algorithm for generalized eigenproblems. J. Comput. Appl. Math. 244, 1\u20139 (2013)","journal-title":"J. Comput. Appl. Math."},{"key":"7_CR51","unstructured":"Kreutzer, M.: Performance engineering for exascale-enabled sparse linear algebra building blocks. Ph.D. Thesis, FAU Erlangen-N\u00fcrnberg, Technische Fakult\u00e4t, Erlangen (2018). https:\/\/doi.org\/10.25593\/978-3-96147-104-1"},{"issue":"5","key":"7_CR52","doi-asserted-by":"crossref","first-page":"C401","DOI":"10.1137\/130930352","volume":"36","author":"M Kreutzer","year":"2014","unstructured":"Kreutzer, M., Hager, G., Wellein, G., Fehske, H., Bishop, A.: A unified sparse matrix data format for efficient general sparse matrix-vector multiplication on modern processors with wide SIMD units. SIAM J. Sci. Comput. 36(5), C401\u2013C423 (2014). https:\/\/doi.org\/10.1137\/130930352","journal-title":"SIAM J. Sci. Comput."},{"key":"7_CR53","doi-asserted-by":"publisher","unstructured":"Kreutzer, M., Pieper, A., Hager, G., Wellein, G., Alvermann, A., Fehske, H.: Performance engineering of the Kernel Polynomal Method on large-scale CPU-GPU systems. In: 2015 IEEE International Parallel and Distributed Processing Symposium, pp. 417\u2013426 (2015). https:\/\/doi.org\/10.1109\/IPDPS.2015.76","DOI":"10.1109\/IPDPS.2015.76"},{"key":"7_CR54","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1007\/978-3-319-40528-5_14","volume-title":"Software for Exascale Computing\u2014SPPEXA 2013\u20132015","author":"M Kreutzer","year":"2016","unstructured":"Kreutzer, M., Thies, J., Pieper, A., Alvermann, A., Galgon, M., R\u00f6hrig-Z\u00f6llner, M., Shahzad, F., Basermann, A., Bishop, A.R., Fehske, H., Hager, G., Lang, B., Wellein, G.: Performance engineering and energy efficiency of building blocks for large, sparse eigenvalue computations on heterogeneous supercomputers. In: Bungartz, H.J., Neumann, P., Nagel, W.E. (eds.) Software for Exascale Computing\u2014SPPEXA 2013\u20132015, pp. 317\u2013338. Springer, Cham (2016). https:\/\/doi.org\/10.1007\/978-3-319-40528-5_14"},{"issue":"5","key":"7_CR55","doi-asserted-by":"crossref","first-page":"1046","DOI":"10.1007\/s10766-016-0464-z","volume":"45","author":"M Kreutzer","year":"2017","unstructured":"Kreutzer, M., Thies, J., R\u00f6hrig-Z\u00f6llner, M., Pieper, A., Shahzad, F., Galgon, M., Basermann, A., Fehske, H., Hager, G., Wellein, G.: GHOST: building blocks for high performance sparse linear algebra on heterogeneous systems. Int. J. Parallel Program. 45(5), 1046\u20131072 (2017). https:\/\/doi.org\/10.1007\/s10766-016-0464-z","journal-title":"Int. J. Parallel Program."},{"key":"7_CR56","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1007\/978-3-319-92040-5_17","volume-title":"High Performance Computing","author":"M Kreutzer","year":"2018","unstructured":"Kreutzer, M., Ernst, D., Bishop, A.R., Fehske, H., Hager, G., Nakajima, K., Wellein, G.: Chebyshev filter diagonalization on modern manycore processors and GPGPUs. In: Yokota, R., Weiland, M., Keyes, D., Trinitis, C. (eds.) High Performance Computing, pp. 329\u2013349. Springer, Cham (2018). https:\/\/dx.doi.org\/10.1007\/978-3-319-92040-5_17"},{"key":"7_CR57","unstructured":"Li, R., Xi, Y., Erlandson, L., Saad, Y.: The Eigenvalues Slicing Library (EVSL): algorithms, implementation, and software (preprint). http:\/\/www-users.cs.umn.edu\/~saad\/software\/EVSL\/index.html"},{"key":"7_CR58","unstructured":"Matrix Market: https:\/\/math.nist.gov\/MatrixMarket\/ . Accessed 26 July 2019"},{"key":"7_CR59","unstructured":"Meila, M., Koelle, S., Zhang, H.: A regression approach for explaining manifold embedding coordinates (2018, e-prints). arXiv:1811.11891"},{"key":"7_CR60","first-page":"601","volume-title":"Numerical Mathematics and Advanced Applications \u2013 ENUMATH 2013. Lecture Notes in Computational Science and Engineering","author":"S M\u00fcthing","year":"2014","unstructured":"M\u00fcthing, S., Ribbrock, D., G\u00f6ddeke, D.: Integrating multi-threading and accelerators into DUNE-ISTL. In: Abdulle, A., Deparis, S., Kressner, D., Nobile, F., Picasso, M., Quarteroni, A. (eds.) Numerical Mathematics and Advanced Applications \u2013 ENUMATH 2013. Lecture Notes in Computational Science and Engineering, vol. 103, pp. 601\u2013609. Springer, Berlin (2014). https:\/\/doi.org\/10.1007\/978-3-319-10705-9_59"},{"key":"7_CR61","unstructured":"ParMETIS - parallel graph partitioning and fill-reducing matrix ordering. http:\/\/glaros.dtc.umn.edu\/gkhome\/metis\/parmetis\/overview"},{"key":"7_CR62","doi-asserted-by":"crossref","first-page":"226","DOI":"10.1016\/j.jcp.2016.08.027","volume":"325","author":"A Pieper","year":"2016","unstructured":"Pieper, A., Kreutzer, M., Alvermann, A., Galgon, M., Fehske, H., Hager, G., Lang, B., Wellein, G.: High-performance implementation of Chebyshev filter diagonalization for interior eigenvalue computations. J. Comput. Phys. 325, 226\u2013243 (2016). http:\/\/dx.doi.org\/10.1016\/j.jcp.2016.08.027","journal-title":"J. Comput. Phys."},{"issue":"11","key":"7_CR63","doi-asserted-by":"publisher","first-page":"115112","DOI":"10.1103\/PhysRevB.79.115112","volume":"79","author":"E Polizzi","year":"2009","unstructured":"Polizzi, E.: Density-matrix-based algorithm for solving eigenvalue problems. Phys. Rev. B 79(11), 115112 (2009). https:\/\/doi.org\/10.1103\/PhysRevB.79.115112","journal-title":"Phys. Rev. B"},{"issue":"6","key":"7_CR64","doi-asserted-by":"crossref","first-page":"206","DOI":"10.1137\/140976017","volume":"37","author":"M R\u00f6hrig-Z\u00f6llner","year":"2015","unstructured":"R\u00f6hrig-Z\u00f6llner, M., Thies, J., Kreutzer, M., Alvermann, A., Pieper, A., Basermann, A., Hager, G., Wellein, G., Fehske, H.: Increasing the performance of the Jacobi-Davidson method by blocking. SIAM J. Sci. Comput. 37(6), 206\u2013239 (2015). http:\/\/dx.doi.org\/10.1137\/140976017","journal-title":"SIAM J. Sci. Comput."},{"key":"7_CR65","doi-asserted-by":"crossref","unstructured":"Sakurai, T., Sugiura, H.: A projection method for generalized eigenvalue problems using numerical integration. J. Comput. Appl. Math. 159(1), 119\u2013128 (2003). https:\/\/doi.org\/10.1016\/S0377-0427(03)00565-X . Sixth Japan-China Joint Seminar on Numerical Mathematics; In Search for the Frontier of Computational and Applied Mathematics toward the 21st Century","DOI":"10.1016\/S0377-0427(03)00565-X"},{"key":"7_CR66","doi-asserted-by":"publisher","first-page":"76","DOI":"10.14495\/jsiaml.1.76","volume":"1","author":"T Sakurai","year":"2009","unstructured":"Sakurai, T., Asakura, J., Tadano, H., Ikegami, T.: Error analysis for a matrix pencil of Hankel matrices with perturbed complex moments. JSIAM Lett. 1, 76\u201379 (2009). https:\/\/doi.org\/10.14495\/jsiaml.1.76","journal-title":"JSIAM Lett."},{"key":"7_CR67","doi-asserted-by":"crossref","unstructured":"Sakurai, T., Futamura, Y., Imakura, A., Imamura, T.: Scalable Eigen-Analysis Engine for Large-Scale Eigenvalue Problems, pp. 37\u201357. Springer, Singapore (2019). https:\/\/doi.org\/10.1007\/978-981-13-1924-2_3","DOI":"10.1007\/978-981-13-1924-2_3"},{"key":"7_CR68","doi-asserted-by":"crossref","unstructured":"Sato, K., et al.: Design and modeling of a non-blocking checkpointing system. In: Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis, pp. 19:1\u201319:10. IEEE Computer Society Press, Los Alamitos (2012)","DOI":"10.1109\/SC.2012.46"},{"issue":"1","key":"7_CR69","doi-asserted-by":"crossref","first-page":"158","DOI":"10.1023\/A:1022326604210","volume":"40","author":"O Schenk","year":"2000","unstructured":"Schenk, O., G\u00e4rtner, K., Fichtner, W.: Efficient sparse LU factorization with left-right looking strategy on shared memory multiprocessors. BIT Numer. Math. 40(1), 158\u2013176 (2000). https:\/\/doi.org\/10.1023\/A:1022326604210","journal-title":"BIT Numer. Math."},{"key":"7_CR70","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1103\/RevModPhys.77.259","volume":"77","author":"U Schollw\u00f6ck","year":"2005","unstructured":"Schollw\u00f6ck, U.: The density-matrix renormalization group. Rev. Mod. Phys. 77, 259\u2013315 (2005)","journal-title":"Rev. Mod. Phys."},{"key":"7_CR71","unstructured":"SCOTCH: Static mapping, graph, mesh and hypergraph partitioning, and parallel and sequential sparse matrix ordering package. http:\/\/www.labri.fr\/perso\/pelegrin\/scotch\/"},{"key":"7_CR72","unstructured":"Shahzad, F.: Checkpoint\/restart and automatic fault tolerance (CRAFT) library. https:\/\/bitbucket.org\/essex\/craft . Accessed 27 July 2017"},{"issue":"3","key":"7_CR73","doi-asserted-by":"publisher","first-page":"501","DOI":"10.1109\/TPDS.2018.2866794","volume":"30","author":"F Shahzad","year":"2019","unstructured":"Shahzad, F., Thies, J., Kreutzer, M., Zeiser, T., Hager, G., Wellein, G.: CRAFT: a library for easier application-level checkpoint\/restart and automatic fault tolerance. IEEE Trans. Parallel Distrib. Syst. 30(3), 501\u2013514 (2019). https:\/\/doi.org\/10.1109\/TPDS.2018.2866794","journal-title":"IEEE Trans. Parallel Distrib. Syst."},{"key":"7_CR74","unstructured":"Song, W.: Matrix-based techniques for (flow-)transition studies. Ph.D. Thesis, University of Groningen (2019). https:\/\/elib.dlr.de\/125176\/"},{"key":"7_CR75","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1016\/j.cnsns.2018.01.003","volume":"60","author":"W Song","year":"2018","unstructured":"Song, W., Wubs, F.W., Thies, J., Baars, S.: Numerical bifurcation analysis of a 3D Turing-type reaction-diffusion model. Commun. Nonlinear Sci. Numer. Simul. 60, 145-164 (2018). https:\/\/doi.org\/10.1016\/j.cnsns.2018.01.003","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"issue":"2","key":"7_CR76","doi-asserted-by":"crossref","first-page":"354","DOI":"10.1137\/13090866X","volume":"35","author":"PTP Tang","year":"2014","unstructured":"Tang, P.T.P., Polizzi, E.: FEAST as a subspace iteration eigensolver accelerated by approximate spectral projection. SIAM J. Matrix Anal. Appl. 35(2), 354\u2013390 (2014). https:\/\/doi.org\/10.1137\/13090866X","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"7_CR77","doi-asserted-by":"crossref","unstructured":"Thies, J., Galgon, M., Shahzad, F., Alvermann, A., Kreutzer, M., Pieper, A., R\u00f6hrig-Z\u00f6llner, M., Basermann, A., Fehske, H., Hager, G., Lang, B., Wellein, G.: Towards an exascale enabled sparse solver repository (2016). In: Software for Exascale Computing \u2013 SPPEXA 2013-2015, Volume 113 of the series Lecture Notes in Computational Science and Engineering, 295-316 (2016). http:\/\/doi.org\/10.1007\/978-3-319-40528-5_13 . Preprint: https:\/\/elib.dlr.de\/100211\/","DOI":"10.1007\/978-3-319-40528-5_13"},{"key":"7_CR78","unstructured":"Thies, J., R\u00f6hrig-Z\u00f6llner, M., Overmars, N., Basermann, A., Ernst, D., Hager, G., Wellein, G.: PHIST: a pipelined, hybrid-parallel iterative solver toolkit. Accepted for publication in ACM Trans. Math. Softw. Preprint: https:\/\/elib.dlr.de\/123323\/"},{"key":"7_CR79","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511615115","volume-title":"Iterative Krylov methods for large linear systems","author":"HA Van der Vorst","year":"2003","unstructured":"Van der Vorst, H.A.: Iterative Krylov methods for large linear systems, vol. 13. Cambridge University Press, Cambridge (2003)"},{"key":"7_CR80","unstructured":"ViennaCL - the Vienna computing library. http:\/\/viennacl.sourceforge.net\/doc\/index.html"},{"key":"7_CR81","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1103\/RevModPhys.78.275","volume":"78","author":"A Wei\u00dfe","year":"2006","unstructured":"Wei\u00dfe, A., Wellein, G., Alvermann, A., Fehske, H.: The kernel polynomial method. Rev. Mod. Phys. 78, 275\u2013306 (2006). https:\/\/link.aps.org\/doi\/10.1103\/RevModPhys.78.275","journal-title":"Rev. Mod. Phys."},{"key":"7_CR82","doi-asserted-by":"crossref","unstructured":"Wouters, M., Vanroose, W.: Automatic exploration techniques for the numerical bifurcation study of the Ginzburg-Landau equation. SIAM J. Dynam. Syst. (2019, submitted). Preprint: https:\/\/arxiv.org\/abs\/1903.02377","DOI":"10.1137\/19M1248467"},{"key":"7_CR83","doi-asserted-by":"publisher","first-page":"41","DOI":"10.14495\/jsiaml.5.41","volume":"5","author":"S Yokota","year":"2013","unstructured":"Yokota, S., Sakurai, T.: A projection method for nonlinear eigenvalue problems using contour integrals. JSIAM Lett. 5, 41\u201344 (2013). https:\/\/doi.org\/10.14495\/jsiaml.5.41","journal-title":"JSIAM Lett."},{"key":"7_CR84","unstructured":"Zoltan: Parallel partitioning, load balancing and data-management services. http:\/\/www.cs.sandia.gov\/zoltan\/Zoltan.html"}],"container-title":["Lecture Notes in Computational Science and Engineering","Software for Exascale Computing - SPPEXA 2016-2019"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-47956-5_7","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,11,5]],"date-time":"2022-11-05T06:05:37Z","timestamp":1667628337000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-030-47956-5_7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020]]},"ISBN":["9783030479558","9783030479565"],"references-count":84,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-47956-5_7","relation":{},"ISSN":["1439-7358","2197-7100"],"issn-type":[{"type":"print","value":"1439-7358"},{"type":"electronic","value":"2197-7100"}],"subject":[],"published":{"date-parts":[[2020]]},"assertion":[{"value":"31 July 2020","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}}]}}