Ritz Value Localization for Non-Hermitian Matrices
Rayleigh-Ritz eigenvalue estimates for Hermitian matrices obey Cauchy interlacing, which has helpful implications for theory, applications, and algorithms. In contrast, few results about the Ritz values of non-Hermitian matrices are known, beyond the containment of these values within the numerical range. To show that such Ritz values enjoy considerable structure, we establish regions within the numerical range in which the various Ritz values of general matrices must be contained. To demonstrate that localization occurs even for extreme examples, we carefully analyze possible Ritz value combinations for a three-dimensional Jordan block.
Citable link to this pagehttps://hdl.handle.net/1911/102191
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