Quadratic Residual Bounds for the Hermitian Eigenvalue Problem
Let \[ A = \left[ \begin{array}{cc} M & R \\ R^{\ast} & N \end{array} \right] {\rm and } \tilde{A} = \left[ \begin{array}{cc} M & 0 \\ 0 & N \end{array} \right] \] be Hermitian matrices. Stronger and more general $O(\|R\|^2)$ bounds relating the eigenvalues of A and A are proved usin...
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| Veröffentlicht in: | SIAM journal on matrix analysis and applications 1998-04, Vol.19 (2), p.541-550 |
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| container_title | SIAM journal on matrix analysis and applications |
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| creator | Mathias, Roy |
| description | Let \[ A = \left[ \begin{array}{cc} M & R \\ R^{\ast} & N \end{array} \right] {\rm and } \tilde{A} = \left[ \begin{array}{cc} M & 0 \\ 0 & N \end{array} \right] \] be Hermitian matrices. Stronger and more general $O(\|R\|^2)$ bounds relating the eigenvalues of A and A are proved using a Schur complement technique. These results extend to singular values, to eigenvalues of non-Hermitian matrices, and to generalized eigenvalues. |
| doi_str_mv | 10.1137/S0895479896310536 |
| format | Article |
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Stronger and more general $O(\|R\|^2)$ bounds relating the eigenvalues of A and A are proved using a Schur complement technique. These results extend to singular values, to eigenvalues of non-Hermitian matrices, and to generalized eigenvalues.</description><identifier>ISSN: 0895-4798</identifier><identifier>EISSN: 1095-7162</identifier><identifier>DOI: 10.1137/S0895479896310536</identifier><language>eng</language><publisher>Philadelphia: Society for Industrial and Applied Mathematics</publisher><subject>Eigenvalues ; Inequality ; Linear algebra ; Matrix</subject><ispartof>SIAM journal on matrix analysis and applications, 1998-04, Vol.19 (2), p.541-550</ispartof><rights>[Copyright] © 1998 Society for Industrial and Applied Mathematics</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c270t-ff78b5d8c631fe6eb8e0ff2d08abb326a89cdcf3ea67d95052f8b5fad30e747e3</citedby><cites>FETCH-LOGICAL-c270t-ff78b5d8c631fe6eb8e0ff2d08abb326a89cdcf3ea67d95052f8b5fad30e747e3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,776,780,3171,27903,27904</link.rule.ids></links><search><creatorcontrib>Mathias, Roy</creatorcontrib><title>Quadratic Residual Bounds for the Hermitian Eigenvalue Problem</title><title>SIAM journal on matrix analysis and applications</title><description>Let \[ A = \left[ \begin{array}{cc} M & R \\ R^{\ast} & N \end{array} \right] {\rm and } \tilde{A} = \left[ \begin{array}{cc} M & 0 \\ 0 & N \end{array} \right] \] be Hermitian matrices. 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and } \tilde{A} = \left[ \begin{array}{cc} M & 0 \\ 0 & N \end{array} \right] \] be Hermitian matrices. Stronger and more general $O(\|R\|^2)$ bounds relating the eigenvalues of A and A are proved using a Schur complement technique. These results extend to singular values, to eigenvalues of non-Hermitian matrices, and to generalized eigenvalues.</abstract><cop>Philadelphia</cop><pub>Society for Industrial and Applied Mathematics</pub><doi>10.1137/S0895479896310536</doi><tpages>10</tpages></addata></record> |
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| issn | 0895-4798 1095-7162 |
| language | eng |
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| source | SIAM Journals Online; Business Source Complete |
| subjects | Eigenvalues Inequality Linear algebra Matrix |
| title | Quadratic Residual Bounds for the Hermitian Eigenvalue Problem |
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