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Softw."],"published-print":{"date-parts":[[2021,9,30]]},"abstract":"<jats:p>SLEPc is a parallel library for the solution of various types of large-scale eigenvalue problems. Over the past few years, we have been developing a module within SLEPc, called NEP, that is intended for solving nonlinear eigenvalue problems. These problems can be defined by means of a matrix-valued function that depends nonlinearly on a single scalar parameter. We do not consider the particular case of polynomial eigenvalue problems (which are implemented in a different module in SLEPc) and focus here on rational eigenvalue problems and other general nonlinear eigenproblems involving square roots or any other nonlinear function. The article discusses how the NEP module has been designed to fit the needs of applications and provides a description of the available solvers, including some implementation details such as parallelization. Several test problems coming from real applications are used to evaluate the performance and reliability of the solvers.<\/jats:p>","DOI":"10.1145\/3447544","type":"journal-article","created":{"date-parts":[[2021,6,26]],"date-time":"2021-06-26T16:14:12Z","timestamp":1624724052000},"page":"1-29","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":9,"title":["NEP"],"prefix":"10.1145","volume":"47","author":[{"given":"Carmen","family":"Campos","sequence":"first","affiliation":[{"name":"Universitat Polit\u00e8cnica de Val\u00e8ncia, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1144-6772","authenticated-orcid":false,"given":"Jose E.","family":"Roman","sequence":"additional","affiliation":[{"name":"Universitat Polit\u00e8cnica de Val\u00e8ncia, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2021,6,26]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479899358194"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2019.109220"},{"key":"e_1_2_1_3_1","volume-title":"Technical Report ANL-95\/11 - Revision 3.13. 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Robust Rational Approximations of Nonlinear Eigenvalue Problems. Technical Report MIMS EPrint 2020.24. The University of Manchester. Retrieved from http:\/\/eprints.maths.manchester.ac.uk\/2796\/.  S. G\u00fcttel G. M. Negri Porzio and F. Tisseur. 2020. Robust Rational Approximations of Nonlinear Eigenvalue Problems. Technical Report MIMS EPrint 2020.24. The University of Manchester. Retrieved from http:\/\/eprints.maths.manchester.ac.uk\/2796\/."},{"key":"e_1_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0962492917000034"},{"key":"e_1_2_1_16_1","doi-asserted-by":"publisher","DOI":"10.1137\/130935045"},{"key":"e_1_2_1_17_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.parco.2007.04.004"},{"key":"e_1_2_1_18_1","doi-asserted-by":"publisher","DOI":"10.1145\/1089014.1089019"},{"key":"e_1_2_1_19_1","volume-title":"Functions of Matrices: Theory and Computation","author":"Higham N. J.","unstructured":"N. J. Higham . 2008. Functions of Matrices: Theory and Computation . 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