{"title":"Approximation of Functional-Algebraic Eigenvalue Problems","authors":"D. M. Korosteleva","doi":"10.1134/s0012266124050100","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We propose a new symmetric variational functional-algebraic statement of the eigenvalue\nproblem in a Hilbert space with a linear dependence on the spectral parameter for a class of\nmathematical models of thin-walled structures with an attached oscillator. The existence of\neigenvalues and eigenvectors is established. A new symmetric approximation of the problem in\na finite-dimensional subspace with a linear dependence on the spectral parameter is constructed.\nError estimates are obtained for the approximate eigenvalues and eigenvectors. The theoretical\nresults are illustrated with an example of a structural mechanics problem.\n</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0012266124050100","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We propose a new symmetric variational functional-algebraic statement of the eigenvalue
problem in a Hilbert space with a linear dependence on the spectral parameter for a class of
mathematical models of thin-walled structures with an attached oscillator. The existence of
eigenvalues and eigenvectors is established. A new symmetric approximation of the problem in
a finite-dimensional subspace with a linear dependence on the spectral parameter is constructed.
Error estimates are obtained for the approximate eigenvalues and eigenvectors. The theoretical
results are illustrated with an example of a structural mechanics problem.
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