Carden, Russell L.Embree, Mark2013-07-112013-07-112012Carden, Russell L. and Embree, Mark. "Ritz Value for Non-Hermitian Matrices." <i>SIAM Journal on Matrix Analysis and Applications,</i> 33, no. 4 (2012) Society for Industrial and Applied Mathematics: 1320-1338. http://dx.doi.org/10.1137/120872693.https://hdl.handle.net/1911/71532Rayleigh-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 their containment within the numerical range. To show that such Ritz values enjoy considerable structure, we establish regions within the numerical range in which certain 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.engArticle is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.Journal articleRitz valuesnumerical rangeinverse field of values problemhttp://dx.doi.org/10.1137/120872693