On Logarithmic Norms

Previous article Next article On Logarithmic NormsTorsten StrömTorsten Strömhttps://doi.org/10.1137/0712055PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractThis paper discusses some normlike properties of the logarithmic norm and related efficiency questions. Some computational questions are raised and some examples of use are indicated.1 F. L. Bauer, , J. Stoer and , C. Witzgall, Absolute and monotonic norms, Numer. Math., 3 (1961), 257–264 10.1007/BF01386026 MR0130104 0111.01602 CrossrefGoogle Scholar2 R. Bellman, Stability Theory of Differential Equations, McGraw-Hill, New York, 1965 Google Scholar3 Richard Bellman, Introduction to matrix analysis, McGraw-Hill Book Co., Inc., New York, 1960xx+328 MR0122820 0124.01001 Google Scholar4 G. J. Cooper, Error bounds for numerical solutions of ordinary differential equations, Numer. Math., 18 (1971/72), 162–170 10.1007/BF01436325 MR0301938 0252.65059 CrossrefISIGoogle Scholar5 W. A. Coppel, Stability and asymptotic behavior of differential equations, D. C. Heath and Co., Boston, Mass., 1965viii+166 MR0190463 0154.09301 Google Scholar6 G. Dahlquist, Stability and error bounds in the numerical integration of ordinary differential equations, Diss., (1958), , reprinted in Trans. Royal Inst. of Technology, No. 130, Stockholm, Sweden, 1959 Google Scholar7 Germund G. Dahlquist, D. Greenspan, On rigorous error bounds in the numerical solution of ordinary differential equationsNumerical Solutions of Nonlinear Differential Equations (Proc. Adv. 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