Nested Bounds for the Spectral Radius

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Previous article Next article Nested Bounds for the Spectral RadiusC. A. Hall and J. SpanierC. A. Hall and J. Spanierhttps://doi.org/10.1137/0705009PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] E. Bodewig, Matrix calculus, North-Holland Publishing Company, Amsterdam, 1956xii+334 MR0080363 Google Scholar[2] D. K. Faddeev and , V. N. Faddeeva, Computational methods of linear algebra, Translated by Robert C. Williams, W. H. Freeman and Co., San Francisco, 1963xi+621 MR0158519 Google Scholar[3] J. M. Hammersley, The numerical reduction of non-singular matrix pencils, Philos. Mag. (7), 40 (1949), 783–807 MR0033608 0032.36101 CrossrefISIGoogle Scholar[4] W. M. Kincaid, Numerical methods for finding characteristic roots and vectors of matrices, Quart. Appl. Math., 5 (1947), 320–345 MR0022452 0029.22202 CrossrefISIGoogle Scholar[5] Richard S. Varga, Matrix iterative analysis, Prentice-Hall Inc., Englewood Cliffs, N.J., 1962xiii+322 MR0158502 Google Scholar[6] J. H. Wilkinson, The algebraic eigenvalue problem, Clarendon Press, Oxford, 1965xviii+662 MR0184422 0258.65037 Google Scholar[7] J. H. Wilkinson, The calculation of the latent roots and vectors of matrices on the pilot model of the A.C.E, Proc. Cambridge Philos. Soc., 50 (1954), 536–566 MR0063775 0056.12202 CrossrefISIGoogle Scholar[8] Tetsuro Yamamoto, A computational method for the dominant root of a nonnegative irreducible matrix, Numer. Math., 8 (1966), 324–333 10.1007/BF02162977 MR0218011 0163.38801 CrossrefISIGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Inequalities of Rayleigh quotients and bounds on the spectral radius of nonnegative symmetric matricesLinear Algebra and its Applications, Vol. 263 Cross Ref Approximations of the Spectral Radius Corresponding Eigenvector, and Second Largest Modulus of an Eigenvalue for Square, Nonnegative, Irreducible MatricesOrna Gross and Uriel G. Rothblum17 July 2006 | SIAM Journal on Matrix Analysis and Applications, Vol. 14, No. 1AbstractPDF (2244 KB)A sequence of lower bounds for the spectral radius of nonnegatfve matricesLinear Algebra and its Applications, Vol. 174 Cross Ref Collatz-Wielandt numbers in general partially ordered spacesLinear Algebra and its Applications, Vol. 173 Cross Ref Computation of bounds for the positive eigenvector of a nonnegative irreducible matrix by monotone iteration1 January 1982 | Mathematics of Computation, Vol. 39, No. 159 Cross Ref A Class of Diagonal Transformation Methods for the Computation of the Spectral Radius of a Nonnegative Irreducible MatrixWolfgang Bunse17 July 2006 | SIAM Journal on Numerical Analysis, Vol. 18, No. 4AbstractPDF (961 KB)Determination of the greatest eigenvalue and the corresponding eigenvector of a non-negative matrixUSSR Computational Mathematics and Mathematical Physics, Vol. 21, No. 4 Cross Ref Regul�re Zerlegungen und Berechnung des Spektralradius nichtnegativer MatrizenNumerische Mathematik, Vol. 34, No. 2 Cross Ref Zur Bestimmung der Frobeniuswurzel nichtnegativer Matrizen1 March 1975 | Computing, Vol. 14, No. 1-2 Cross Ref Reduction of an irreducible non-negative matrix to quasi-stochastic form by the method of similarity variationUSSR Computational Mathematics and Mathematical Physics, Vol. 15, No. 5 Cross Ref Nested bounds for the spectral radiusNumerische Mathematik, Vol. 14, No. 1 Cross Ref Volume 5, Issue 1| 1968SIAM Journal on Numerical Analysis History Submitted:25 January 1967Published online:14 July 2006 InformationCopyright © 1968 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0705009Article page range:pp. 113-125ISSN (print):0036-1429ISSN (online):1095-7170Publisher:Society for Industrial and Applied Mathematics