Previous article Next article Minimal Gerschgorin Sets for Partitioned MatricesRichard S. VargaRichard S. Vargahttps://doi.org/10.1137/0707040PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] J. L. Brenner, Bounds for determinants, Proc. Nat. Acad. Sci. U. S. A., 40 (1954), 452–454 MR0062094 0058.00904 CrossrefISIGoogle Scholar[2] J. L. Brenner, Geršgorin theorems, regularity theorems, and bounds for determinants of partitioned matrices, SIAM J. Appl. Math., 19 (1970), 443–450 10.1137/0119043 MR0268198 0206.03802 LinkISIGoogle Scholar[3] David G. Feingold and , Richard S. Varga, Block diagonally dominant matrices and generalizations of the Gerschgorin circle theorem, Pacific J. Math., 12 (1962), 1241–1250 MR0151473 0109.24802 CrossrefISIGoogle Scholar[4] S. Gerschgorin, Über die Abgrenzung der Eigenwerte einer Matrix, Izv. Akad. Nauk SSSR Ser. Mat., 7 (1931), 749–754 Google Scholar[5] Alston S. Householder, The theory of matrices in numerical analysis, Blaisdell Publishing Co. Ginn and Co. New York-Toronto-London, 1964xi+257 MR0175290 0161.12101 Google Scholar[6] Alston S. Householder, , Richard S. Varga and , James H. Wilkinson, A note on Gershgorin's inclusion theorem for eigenvalues of matrices., Numer. Math., 16 (1970), 141–144 10.1007/BF02308866 MR0275648 CrossrefISIGoogle Scholar[7] B. W. Levinger, Minimal Gerschgorin sets. III, Linear Algebra and Appl., 2 (1969), 13–19 10.1016/0024-3795(69)90003-2 MR0241450 0174.31701 CrossrefGoogle Scholar[8] B. W. Levinger and , R. S. Varga, Minimal Gerschgorin sets. II, Pacific J. Math., 17 (1966), 199–210 MR0194429 0168.03001 CrossrefISIGoogle Scholar[9] F. Robert, Recherche d'une M-matrice parmi les minorantes d'un opérateur linéaire, Numer. Math., 9 (1966), 189–199 10.1007/BF02162083 MR0208821 0156.16206 CrossrefISIGoogle Scholar[10] F. Robert, Masters Thesis, Étude et utilisation de normes vectorielles en analyse numérique linéaire, Doctoral thesis, University of Grenoble, 1968 Google Scholar[11] Richard S. Varga, Matrix iterative analysis, Prentice-Hall Inc., Englewood Cliffs, N.J., 1962xiii+322 MR0158502 0133.08602 Google Scholar[12] Richard S. Varga, Minimal Gerschgorin sets, Pacific J. Math., 15 (1965), 719–729 MR0183728 0168.02904 CrossrefISIGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Nonsingularity/singularity criteria for nonstrictly block diagonally dominant matricesLinear Algebra and its Applications, Vol. 359, No. 1-3 Cross Ref Gershgorin's theorem for matrices of operatorsLinear Algebra and its Applications, Vol. 291, No. 1-3 Cross Ref On a criterion for the nonsingularity of complex matricesLinear Algebra and its Applications, Vol. 173 Cross Ref A nonsingularity criterion for complex matricesLinear Algebra and its Applications, Vol. 168 Cross Ref A Criterion for Nonvanishing of DeterminantsZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 71, No. 7-8 Cross Ref Decomposition and decentralized control system design: A review of frequency domain methods Cross Ref Some simple estimates for singular values of a matrixLinear Algebra and its Applications, Vol. 56 Cross Ref The inverse M-matrix problemLinear Algebra and its Applications, Vol. 18, No. 1 Cross Ref Contraction en norme vectorielle: Convergence d'iterations chaotiques pour des equations non linéaires de point fixe à plusieurs variablesLinear Algebra and its Applications, Vol. 13, No. 1-2 Cross Ref Spectrum localization in Banach spaces ILinear Algebra and its Applications, Vol. 8, No. 3 Cross Ref Gerschgorin theorems for partitioned matricesLinear Algebra and its Applications, Vol. 4, No. 3 Cross Ref Volume 7, Issue 4| 1970SIAM Journal on Numerical Analysis History Submitted:18 November 1969Published online:14 July 2006 InformationCopyright © 1970 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0707040Article page range:pp. 493-507ISSN (print):0036-1429ISSN (online):1095-7170Publisher:Society for Industrial and Applied Mathematics