{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T06:51:54Z","timestamp":1762325514944,"version":"build-2065373602"},"reference-count":31,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2023,1,6]],"date-time":"2023-01-06T00:00:00Z","timestamp":1672963200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Russian Science Foundation","award":["N 22-21-00318"],"award-info":[{"award-number":["N 22-21-00318"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The generalized eigenvalue problem for a symmetric definite matrix pencil obtained from finite-element modeling of electroelastic materials is solved numerically by the Lanczos algorithm. The mass matrix is singular in the considered problem, and therefore the process proceeds with the semi-inner product defined by this matrix. The shift-and-invert Lanczos algorithm is used to find multiple eigenvalues closest to some shift and the corresponding eigenvectors. The results of the numerical experiments are presented.<\/jats:p>","DOI":"10.3390\/sym15010171","type":"journal-article","created":{"date-parts":[[2023,1,9]],"date-time":"2023-01-09T02:31:30Z","timestamp":1673231490000},"page":"171","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["The Numerical Solution of Large-Scale Generalized Eigenvalue Problems Arising from Finite-Element Modeling of Electroelastic Materials"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7073-1162","authenticated-orcid":false,"given":"Tatiana","family":"Martynova","sequence":"first","affiliation":[{"name":"Vorovich Institute of Mathematics, Mechanics and Computer Science, Milchakova Street 8a, Southern Federal University, 344090 Rostov-on-Don, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9816-6759","authenticated-orcid":false,"given":"Galina","family":"Muratova","sequence":"additional","affiliation":[{"name":"Vorovich Institute of Mathematics, Mechanics and Computer Science, Milchakova Street 8a, Southern Federal University, 344090 Rostov-on-Don, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2311-7562","authenticated-orcid":false,"given":"Pavel","family":"Oganesyan","sequence":"additional","affiliation":[{"name":"Vorovich Institute of Mathematics, Mechanics and Computer Science, Milchakova Street 8a, Southern Federal University, 344090 Rostov-on-Don, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1702-065X","authenticated-orcid":false,"given":"Olga","family":"Shtein","sequence":"additional","affiliation":[{"name":"Vorovich Institute of Mathematics, Mechanics and Computer Science, Milchakova Street 8a, Southern Federal University, 344090 Rostov-on-Don, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Sezer, N., and Ko\u00e7, M. 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