Gao, Jing; Li, Chaoqian A new localization set for generalized eigenvalues. (English) Zbl 1381.15006 J. Inequal. Appl. 2017, Paper No. 113, 11 p. (2017). Summary: A new localization set for generalized eigenvalues is obtained. It is shown that the new set is tighter than that in [V. Kostić et al., Numer. Linear Algebra Appl. 16, No. 11–12, 883–898 (2009; Zbl 1224.65094)]. Numerical examples are given to verify the corresponding results. Cited in 1 Document MSC: 15A42 Inequalities involving eigenvalues and eigenvectors 65F15 Numerical computation of eigenvalues and eigenvectors of matrices 15A22 Matrix pencils Keywords:generalized eigenvalue; inclusion set; matrix pencil; numerical examples Citations:Zbl 1224.65094 PDFBibTeX XMLCite \textit{J. Gao} and \textit{C. Li}, J. Inequal. Appl. 2017, Paper No. 113, 11 p. (2017; Zbl 1381.15006) Full Text: DOI References: [1] Kostić, V, Cvetković, LJ, Varga, RS: Geršgorin-type localizations of generalized eigenvalues. Numer. Linear Algebra Appl. 16, 883-898 (2009) · Zbl 1224.65094 [2] Nakatsukasa, Y: Gerschgorin’s theorem for generalized eigenvalue problem in the Euclidean metric. Math. Comput. 80(276), 2127-2142 (2011) · Zbl 1230.15012 [3] Hua, Y, Sarkar, TK: On SVD for estimating generalized eigenvalues of singular matrix pencil in noise. IEEE Trans. Signal Process. 39(4), 892-900 (1991) [4] Mangasarian, OL, Wild, EW: Multisurface proximal support vector machine classification via generalized eigenvalues. IEEE Trans. Pattern Anal. Mach. Intell. 28(1), 69-74 (2006) [5] Qiu, L, Davison, EJ: The stability robustness of generalized eigenvalues. IEEE Trans. Autom. Control 37(6), 886-891 (1992) · Zbl 0775.93181 [6] Hochstenbach, ME: Fields of values and inclusion region for matrix pencils. Electron. Trans. Numer. Anal. 38, 98-112 (2011) · Zbl 1287.65025 [7] Gershgorin, SGW: Theory for the generalized eigenvalue problem Ax=λBx \(Ax=\lambda Bx\). Math. Comput. 29(130), 600-606 (1975) · Zbl 0302.65028 [8] Varga, RS: Geršgorin and His Circles. Springer, Berlin (2004) · Zbl 1057.15023 [9] Melmana, A: An alternative to the Brauer set. Linear Multilinear Algebra 58, 377-385 (2010) · Zbl 1192.15006 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.