Reactor Criticality and Nonnegative Matrices

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Previous article Next article Reactor Criticality and Nonnegative MatricesGarrett Birkhoff and Richard S. VargaGarrett Birkhoff and Richard S. Vargahttps://doi.org/10.1137/0106025PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] C. J. Everett and , S. Ulam, Multiplicative systems. I, Proc. Nat. Acad. Sci. U. S. A., 34 (1948), 403–405 MR0026280 0032.29104 CrossrefISIGoogle Scholar[2] M. Fréchet, Méthode des Fonctions Arbitraires ⋯, Vol. 2, Gauthier-Villars, Paris, 1936 Google Scholar[3] G. Frobenius, Über Matrizen aus nicht negativen Elementen, Sitzungsberichte der Akademie der Wissenschaften zu Berlin, (1912), 456–477 Google Scholar[4] S. Glasstone and , M. C. Edlund, The Elements of Nuclear Reactor Theory, van Nostrand, New York, 1952 Google Scholar[5] T. E. Harris, Some mathematical models for branching processes, Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, 1950, University of California Press, Berkeley and Los Angeles, 1951, 305–328 MR0045331 0045.07701 Google Scholar[6] V. Romanovsky, Recherches sur les chaı⁁nes de Markoff, Acta Math., 66 (1936), 147–251 0014.02802 CrossrefGoogle Scholar[7] R. S. Varga, Numerical solution of the two-group diffusion equation in $x-y$ geometry, Trans. I. R. E., NS-4 (1957), 52–62 MR0102922 Google Scholar[8] A. M. Weinberg, Current status of nuclear reactor theory, Amer. J. Phys., 20 (1952), 1–12 10.1119/1.1933268 0046.44502 CrossrefISIGoogle Scholar[9] Helmut Wielandt, Unzerlegbare, nicht negative Matrizen, Math. Z., 52 (1950), 642–648 10.1007/BF02230720 MR0035265 0035.29101 CrossrefGoogle Scholar[10] David Young, Iterative methods for solving partial difference equations of elliptic type, Trans. Amer. Math. Soc., 76 (1954), 92–111 MR0059635 0055.35704 CrossrefISIGoogle Scholar[11] Gerard Debreu and , I. N. Herstein, Nonnegative square matrices, Econometrica, 21 (1953), 597–607 MR0059240 0051.00901 CrossrefISIGoogle Scholar[12] Garrett Birkhoff and , Richard S. Varga, Reactor criticality and non-negative matrices, Report WAPD-166, Bettis Atomic Power Division of Westing-house Electric Corporation, 1957 Google Scholar[13] M. K. Butler and , J. M. Cook, Univac Programs for the solution of one-dimen-sional multigroup reactor equations, Report ANL-5437, Argonne National Laboratory, 1956 CrossrefGoogle Scholar[14] George G. O'Brien, , Morton A. Hyman and , Sidney Kaplan, A study of the numerical solution of partial differential equations, J. Math. Physics, 29 (1951), 223–251 MR0040805 0042.13204 CrossrefISIGoogle Scholar[15] Stanley P. Frankel, Convergence rates of iterative treatments of partial differential equations, Math. Tables and Other Aids to Computation, 4 (1950), 65–75 MR0046149 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Positivity Preserving Balanced Truncation for Descriptor Systems4 September 2009 | SIAM Journal on Control and Optimization, Vol. 48, No. 4AbstractPDF (323 KB)Pattern Properties and Spectral Inequalities in Max Algebra17 July 2006 | SIAM Journal on Matrix Analysis and Applications, Vol. 16, No. 3AbstractPDF (1601 KB)On Criticality and the Stein–Rosenberg Theorem17 July 2006 | SIAM Journal on Numerical Analysis, Vol. 18, No. 3AbstractPDF (646 KB)New Directions in Linear Differential Equations10 July 2006 | SIAM Review, Vol. 21, No. 1AbstractPDF (1467 KB)Iterative Solution of Elliptic Systems and Applications to the Neutron Diffusion Equations of Reactor Physics (Eugene L. Wachspress)18 July 2006 | SIAM Review, Vol. 9, No. 4AbstractPDF (441 KB)Remarks on the Order of Convergence of Discrete Analogs for Second-Order Elliptic Partial Differential Equations18 July 2006 | SIAM Review, Vol. 4, No. 4AbstractPDF (1024 KB)An Alternating-Direction-Implicit Iteration TechniqueE. L. Wachspress and G. J. Habetler10 July 2006 | Journal of the Society for Industrial and Applied Mathematics, Vol. 8, No. 2AbstractPDF (1508 KB) Volume 6, Issue 4| 1958Journal of the Society for Industrial and Applied Mathematics History Submitted:09 January 1958Published online:10 July 2006 InformationCopyright © 1958 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0106025Article page range:pp. 354-377ISSN (print):0368-4245ISSN (online):2168-3484Publisher:Society for Industrial and Applied Mathematics