Bounds on Changes in Ritz Values for a Perturbed Invariant Subspace of a Hermitian Matrix
The Rayleigh–Ritz method is widely used for eigenvalue approximation. Given a matrix $X$ with columns that form an orthonormal basis for a subspace $\mathcal{X}$, and a Hermitian matrix $A$, th...
The Rayleigh–Ritz method is widely used for eigenvalue approximation. Given a matrix $X$ with columns that form an orthonormal basis for a subspace $\mathcal{X}$, and a Hermitian matrix $A$, th...
Combination Preconditioning and the Bramble–Pasciak$^{+}$ Preconditioner
It is widely appreciated that the iterative solution of linear systems of equations with large sparse matrices is much easier when the matrix is symmetric. It is equally advantageous to employ symmet...
It is widely appreciated that the iterative solution of linear systems of equations with large sparse matrices is much easier when the matrix is symmetric. It is equally advantageous to employ symmet...
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Eigenvalues of the Sum of Matrices from Unitary Similarity Orbits
SIAM. J. Matrix Anal. & Appl. Volume 30, Issue 2, pp. 560-581 (2008)
Published June 6, 2008
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Let $A$ and $B$ be $n\times n$ complex matrices. Characterization is given for the set ${\cal E}(A,B)$ of eigenvalues of matrices of the form $U^*AU+V^*BV$ for some unitary matrices $U$ and $V$. Consequences of the results are discussed and computer algorithms and programs are designed to generate the set ${\cal E}(A,B)$. The results refine those of Wielandt on normal matrices. Extensions of the results to the sum of matrices from three or more unitary similarity orbits are also considered.
©2008 Society for Industrial and Applied Mathematics| History: | Received August 2, 2007; accepted January 2, 2008; published June 6, 2008 |
| Permalink: | http://dx.doi.org/10.1137/070699123 |
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PUBLICATION DATA
0895-4798 (print)
1095-7162 (online)
SIAM