Kagström, Bo Bounds and perturbation bounds for the matrix exponential. (English) Zbl 0356.65034 BIT, Nord. Tidskr. Inf.-behandl. 17, 39-57 (1977). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 29 Documents MSC: 65F99 Numerical linear algebra PDFBibTeX XMLCite \textit{B. Kagström}, BIT, Nord. Tidskr. Inf.-behandl. 17, 39--57 (1977; Zbl 0356.65034) Full Text: DOI References: [1] H. T. Chieh,Evaluation of matrix functions by real similarity transformation, Journal of the Franklin Institute Vol. 295, No 1, 69–79, 1973. · Zbl 0292.65017 · doi:10.1016/0016-0032(73)90253-6 [2] G. Dahlquist,Stability and asymptotic behavior of differential equations, Diss. 1958; reprinted in Trans. Royal Inst. of Technology, No 130, Stockholm, Sweden, 1959. [3] K. C. Daly,Evaluating the matrix exponential, Electronic letters 8, 1972. [4] W. Fair, and Y. L. Luke,Padé approximations to the operator exponential, Numerische Mathematik 14, 379–382, 1970. · Zbl 0181.16702 · doi:10.1007/BF02165592 [5] P. Henrici,Bounds for iterates, inverses, spectral variation and fields of values of non-normal matrices, Numer. Math. 4, 24–40, 1962. · Zbl 0102.01502 · doi:10.1007/BF01386294 [6] R. Jeltsch,On the norm of a matrix exponential. Solution to problem 74–5, SIAM Review Vol 16, No 1, p. 94. Private communication. [7] D. W. Kammler,An algorithm for numerically solving a first order system of linear differential equations with constant coefficients. Private communication. [8] B. Kågström and A. Ruhe,An algorithm for numerical computation of the Jordan normal form of a complex matrix, To appear in ACM Trans. on Mathematical Software. [9] B. Kågström and A. Ruhe,The Fortran program for numerical computation of the Jordan normal form of a complex matrix, Report UMINF-51.74, Dept. Computer Sciences, University of Umeå, Sweden. [10] C. B. Moler,Difficulties in computing the exponential of a matrix, Proceedings of the second USA-Japan Computer Conference, 79–82, 1975. [11] B. N. Parlett,Computation of functions of triangular matrices, Memorandum No ERL-M481, Electronics Research Laboratory, College of Engineering, University of California, Berkeley, 1974. [12] T. Ström,On logarithmic norms, SIAM Journal Numerical Analysis Vol 12, No 5, 741–753, 1975. · Zbl 0321.15012 · doi:10.1137/0712055 [13] T. Ström,On the use of majorants for strict error estimation of numerical solutions to ODE’s, Rep. NA 70.10, Dept. Computer Science, Royal Inst. Tech., Stockholm, Sweden 1970. [14] C. van Loan,A study of the matrix exponential, University of Manchester numerical analysis report 10, 1975, Manchester, England. [15] R. C. Ward,Numerical computation of the matrix exponential with accuracy estimates, Report UCCND-CSD-24, 1975, Oak Ridge National Laboratory, Tennessee. [16] A. Wragg and C. Davies,Computation of the exponential of a matrix I: Theoretical considerations, Journal Inst. Math. Applics. 15, 369–375, 1973. · Zbl 0262.65054 · doi:10.1093/imamat/11.3.369 [17] A. Wragg and C. Davies,Computation of the exponential of a matrix II: Practical considerations, Journal Inst. Math. Applics. 15, 273–278, 1975. · Zbl 0307.65045 · doi:10.1093/imamat/15.3.273 [18] V. Zakian,Rational approximations to the matrix exponential, Electronics Letters vol 6, 814–815, 1970 · doi:10.1049/el:19700561 [19] V. Zakian and R. E. Scraton,Comments on rational approximations to the matrix exponential, Electronics Letters, vol 7, 260–262, 1971. · doi:10.1049/el:19710177 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.