{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,2]],"date-time":"2026-01-02T01:24:42Z","timestamp":1767317082879,"version":"3.48.0"},"publisher-location":"Singapore","reference-count":19,"publisher":"Springer Nature Singapore","isbn-type":[{"value":"9789819556564","type":"print"},{"value":"9789819556571","type":"electronic"}],"license":[{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026]]},"DOI":"10.1007\/978-981-95-5657-1_3","type":"book-chapter","created":{"date-parts":[[2026,1,2]],"date-time":"2026-01-02T01:20:34Z","timestamp":1767316834000},"page":"26-34","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Utilizing Large Language Models for\u00a0Finding All Roots to\u00a0Nonlinear Systems of\u00a0Equations: Solutions, Accuracy, and\u00a0Prompt Design"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2691-4575","authenticated-orcid":false,"given":"Alexander","family":"Semenov","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1593-6931","authenticated-orcid":false,"given":"Michael J.","family":"Hirsch","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9623-8053","authenticated-orcid":false,"given":"Panos M.","family":"Pardalos","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2026,1,2]]},"reference":[{"issue":"92","key":"3_CR1","doi-asserted-by":"publisher","first-page":"577","DOI":"10.1090\/S0025-5718-1965-0198670-6","volume":"19","author":"CG Broyden","year":"1965","unstructured":"Broyden, C.G.: A class of methods for solving nonlinear simultaneous equations. Math. Comput. 19(92), 577\u2013593 (1965)","journal-title":"Math. Comput."},{"key":"3_CR2","doi-asserted-by":"crossref","unstructured":"Dennis, J.E., Schnabel, R.B.: In: Numerical methods for unconstrained optimization and nonlinear equations. SIAM (1996)","DOI":"10.1137\/1.9781611971200"},{"key":"3_CR3","doi-asserted-by":"crossref","unstructured":"Floudas, C.A., Pardalos, P.M.: A collection of test problems for constrained global optimization algorithms. LNCS. Springer (1990)","DOI":"10.1007\/3-540-53032-0"},{"key":"3_CR4","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-3040-1","volume-title":"Handbook of Test Problems in Local and Global Optimization","author":"CA Floudas","year":"1999","unstructured":"Floudas, C.A., et al.: Handbook of Test Problems in Local and Global Optimization. Springer, US (1999)"},{"key":"3_CR5","unstructured":"Hendrycks, D.,\u00a0et al.: Measuring mathematical problem solving with the MATH dataset. In: Proceedings of the 35th Conference on Neural Information Processing Systems (2021)"},{"key":"3_CR6","doi-asserted-by":"publisher","first-page":"437","DOI":"10.1090\/S0002-9904-1902-00923-3","volume":"8","author":"D Hilbert","year":"1902","unstructured":"Hilbert, D.: Mathematical problems. Bull. Am. Math. Soc. 8, 437\u2013479 (1902)","journal-title":"Bull. Am. Math. Soc."},{"issue":"4","key":"3_CR7","doi-asserted-by":"publisher","first-page":"2000","DOI":"10.1016\/j.nonrwa.2008.03.006","volume":"10","author":"MJ Hirsch","year":"2009","unstructured":"Hirsch, M.J., Pardalos, P.M., Resende, M.G.C.: Solving systems of nonlinear equations with continuous GRASP. Nonlinear Anal. Real World Appl. 10(4), 2000\u20132006 (2009)","journal-title":"Nonlinear Anal. Real World Appl."},{"key":"3_CR8","unstructured":"Hirsch, M.J., Semenov, A., Trevena, W., Pardalos, P.M.: A method to generate a general system of nonlinear equations with known solutions. submitted (2025)"},{"issue":"4","key":"3_CR9","doi-asserted-by":"publisher","first-page":"345","DOI":"10.1023\/A:1024463631728","volume":"4","author":"C Jansson","year":"1998","unstructured":"Jansson, C.: An NP-hardness result for nonlinear systems. Reliable Comput. 4(4), 345\u2013350 (1998)","journal-title":"Reliable Comput."},{"key":"3_CR10","unstructured":"Kotsireas, I., Pardalos, P.M., Semenov, A., Trevena, W., \u00a0Vrahatis, M.: Survey of methods for solving systems of nonlinear equations, part I: root-finding approaches. arXiv (2022)"},{"key":"3_CR11","unstructured":"Kotsireas, I., Pardalos, P.M., Semenov, A., Trevena, W., Vrahatis, M.: Survey of methods for solving systems of nonlinear equations, part II: optimization-based approaches. arXiv (2022)"},{"key":"3_CR12","unstructured":"Li, J.: Numinamath: The largest public dataset in ai4maths with 860k pairs of competition math problems and solutions. Hugging Face repository (2024). Dataset available at https:\/\/huggingface.co\/datasets\/numinamath. Accessed 17 July 2025"},{"issue":"2","key":"3_CR13","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1287\/ijoc.2018.0876","volume":"31","author":"J Pei","year":"2019","unstructured":"Pei, J., Dra\u017ei\u0107, Z., Dra\u017ei\u0107, M., Mladenovi\u0107, N., Pardalos, P.M.: Continuous variable neighborhood search (c-vns) for solving systems of nonlinear equations. INFORMS J. Comput. 31(2), 235\u2013250 (2019)","journal-title":"INFORMS J. Comput."},{"key":"3_CR14","unstructured":"Schick, T., et al.: Toolformer: Language models can teach themselves to use tools (2023)"},{"key":"3_CR15","unstructured":"Touvron, H., et al.: LLaMA: Open and efficient foundation language models (2023)"},{"key":"3_CR16","unstructured":"Vaswani, A., et al.: Attention is all you need (2023)"},{"key":"3_CR17","unstructured":"Wang, H.,\u00a0Feng, S.,\u00a0He, T., Tan, Z., Han, X., Tsvetkov, Y.: Can language models solve graph problems in natural language? In: Thirty-seventh Conference on Neural Information Processing Systems (2023)"},{"key":"3_CR18","unstructured":"Ye, Y., Huang, Z., Xiao, Y., Chern, E., Xia, S., Liu, P.: Limo: Less is more for reasoning (2025)"},{"key":"3_CR19","doi-asserted-by":"crossref","unstructured":"Zhang, Y., Wang, H., Feng, S., Tan, Z., Han, X., He, T., Tsvetkov, Y.: Can LLM graph reasoning generalize beyond pattern memorization? (2024)","DOI":"10.18653\/v1\/2024.findings-emnlp.127"}],"container-title":["Lecture Notes in Computer Science","Algorithmic Aspects in Information and Management"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-981-95-5657-1_3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,2]],"date-time":"2026-01-02T01:20:36Z","timestamp":1767316836000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-981-95-5657-1_3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026]]},"ISBN":["9789819556564","9789819556571"],"references-count":19,"URL":"https:\/\/doi.org\/10.1007\/978-981-95-5657-1_3","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026]]},"assertion":[{"value":"2 January 2026","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"AAIM","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Algorithmic Aspects in Information and Management","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Ulaanbaatar","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Mongolia","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2025","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"23 June 2025","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"26 June 2025","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"19","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"aaim2025","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/www.aaim2025.org\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}