{"title":"一类拟势方程伽辽金近似的渐近误差界","authors":"E.P. Zhidov, E.G. Nikonov, B.N. Khoromskii","doi":"10.1016/0041-5553(90)90201-3","DOIUrl":null,"url":null,"abstract":"<div><p>Error bounds for the Galerkin approximation of solutions to the eigenvalue problem are derived for a class of quasipotential integral equations. In the case of completely continuous operators conditions are derived under which the error in the approximate solutions of a spectral problem can be expanded in powers of a parameter <em>r</em><sup>−1</sup>,where <em>r</em> is the length of the discretization interval of the integral operator, which is defined on a half-line.</p></div>","PeriodicalId":101271,"journal":{"name":"USSR Computational Mathematics and Mathematical Physics","volume":"30 3","pages":"Pages 133-140"},"PeriodicalIF":0.0000,"publicationDate":"1990-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0041-5553(90)90201-3","citationCount":"0","resultStr":"{\"title\":\"Asymptotic error bounds in Galerkin approximation for a certain class of quasipotential equations\",\"authors\":\"E.P. Zhidov, E.G. Nikonov, B.N. Khoromskii\",\"doi\":\"10.1016/0041-5553(90)90201-3\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Error bounds for the Galerkin approximation of solutions to the eigenvalue problem are derived for a class of quasipotential integral equations. In the case of completely continuous operators conditions are derived under which the error in the approximate solutions of a spectral problem can be expanded in powers of a parameter <em>r</em><sup>−1</sup>,where <em>r</em> is the length of the discretization interval of the integral operator, which is defined on a half-line.</p></div>\",\"PeriodicalId\":101271,\"journal\":{\"name\":\"USSR Computational Mathematics and Mathematical Physics\",\"volume\":\"30 3\",\"pages\":\"Pages 133-140\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1990-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/0041-5553(90)90201-3\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"USSR Computational Mathematics and Mathematical Physics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/0041555390902013\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"USSR Computational Mathematics and Mathematical Physics","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/0041555390902013","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Asymptotic error bounds in Galerkin approximation for a certain class of quasipotential equations
Error bounds for the Galerkin approximation of solutions to the eigenvalue problem are derived for a class of quasipotential integral equations. In the case of completely continuous operators conditions are derived under which the error in the approximate solutions of a spectral problem can be expanded in powers of a parameter r−1,where r is the length of the discretization interval of the integral operator, which is defined on a half-line.
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