Pseudoinverse formulation of Rayleigh-Schrödinger perturbation theory for the symmetric matrix eigenvalue problem
A comprehensive treatment of Rayleigh-Schrödinger perturbation theory for the symmetric matrix eigenvalue problem is furnished with emphasis on the degenerate problem. The treatment is simply based upon the Moore-Penrose pseudoinverse thus distinguishing it from alternative approaches in the literat...
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| Format: | Article |
| Language: | English |
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Wiley
2003-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/S1110757X03303092 |
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| _version_ | 1832556758436937728 |
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| author | Brian J. McCartin |
| author_facet | Brian J. McCartin |
| author_sort | Brian J. McCartin |
| collection | DOAJ |
| description | A comprehensive treatment of Rayleigh-Schrödinger perturbation theory for the symmetric matrix eigenvalue problem is furnished with emphasis on the degenerate problem. The treatment is simply based upon the Moore-Penrose pseudoinverse thus distinguishing it from alternative approaches in the literature. In addition to providing a concise matrix-theoretic formulation of this procedure, it also provides for the explicit determination of that stage of the algorithm where each higher-order eigenvector correction becomes fully determined. The theory is built up gradually with each successive stage appended with an illustrative example. |
| format | Article |
| id | doaj-art-8f69b11210c74b4d859820c1e3640be2 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2003-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-8f69b11210c74b4d859820c1e3640be22025-02-03T05:44:33ZengWileyJournal of Applied Mathematics1110-757X1687-00422003-01-012003945948510.1155/S1110757X03303092Pseudoinverse formulation of Rayleigh-Schrödinger perturbation theory for the symmetric matrix eigenvalue problemBrian J. McCartin0Applied Mathematics, Kettering University, 1700 West Third Avenue, Flint 48504-4898, MI, USAA comprehensive treatment of Rayleigh-Schrödinger perturbation theory for the symmetric matrix eigenvalue problem is furnished with emphasis on the degenerate problem. The treatment is simply based upon the Moore-Penrose pseudoinverse thus distinguishing it from alternative approaches in the literature. In addition to providing a concise matrix-theoretic formulation of this procedure, it also provides for the explicit determination of that stage of the algorithm where each higher-order eigenvector correction becomes fully determined. The theory is built up gradually with each successive stage appended with an illustrative example.http://dx.doi.org/10.1155/S1110757X03303092 |
| spellingShingle | Brian J. McCartin Pseudoinverse formulation of Rayleigh-Schrödinger perturbation theory for the symmetric matrix eigenvalue problem Journal of Applied Mathematics |
| title | Pseudoinverse formulation of Rayleigh-Schrödinger perturbation
theory for the symmetric matrix eigenvalue problem |
| title_full | Pseudoinverse formulation of Rayleigh-Schrödinger perturbation
theory for the symmetric matrix eigenvalue problem |
| title_fullStr | Pseudoinverse formulation of Rayleigh-Schrödinger perturbation
theory for the symmetric matrix eigenvalue problem |
| title_full_unstemmed | Pseudoinverse formulation of Rayleigh-Schrödinger perturbation
theory for the symmetric matrix eigenvalue problem |
| title_short | Pseudoinverse formulation of Rayleigh-Schrödinger perturbation
theory for the symmetric matrix eigenvalue problem |
| title_sort | pseudoinverse formulation of rayleigh schrodinger perturbation theory for the symmetric matrix eigenvalue problem |
| url | http://dx.doi.org/10.1155/S1110757X03303092 |
| work_keys_str_mv | AT brianjmccartin pseudoinverseformulationofrayleighschrodingerperturbationtheoryforthesymmetricmatrixeigenvalueproblem |