Stability and semipositivity of real matrices
HTML articles powered by AMS MathViewer
- by Abraham Berman and Robert C. Ward PDF
- Bull. Amer. Math. Soc. 83 (1977), 262-263
References
- G . P. Barker, A. Berman, and R. J. Plemmons, Positive diagonal solutions to the Lyapunov equations, Linear and Multilinear Algebra 5 (1977/78), no. 4, 249–256. MR 469939, DOI 10.1080/03081087808817203
- Miroslav Fiedler and Vlastimil Pták, On matrices with non-positive off-diagonal elements and positive principal minors, Czechoslovak Math. J. 12(87) (1962), 382–400 (English, with Russian summary). MR 142565, DOI 10.21136/CMJ.1962.100526
- Charles R. Johnson, Second, third, and fourth order $D$-stability, J. Res. Nat. Bur. Standards Sect. B 78B (1974), 11–13. MR 340287, DOI 10.6028/jres.078B.004 4. A. M. Lyapunov (1892), Problème général de la stabilité du mouvement, Comm. Math. Soc. Kharkow; English transl., Ann. of Math. Studies, no. 17, Princeton Univ. Press, Princeton, N. J.; Oxford Univ. Press, London, 1947. MR 9, 34.
- Olga Taussky, A remark on a theorem of Lyapunov, J. Math. Anal. Appl. 2 (1961), 105–107. MR 124335, DOI 10.1016/0022-247X(61)90048-8
- James S. Vandergraft, Applications of partial orderings to the study of positive definiteness, monotonicity, and convergence of iterative methods for linear systems, SIAM J. Numer. Anal. 9 (1972), 97–104. MR 309971, DOI 10.1137/0709011
Additional Information
- Journal: Bull. Amer. Math. Soc. 83 (1977), 262-263
- MSC (1970): Primary 15A48; Secondary 15A15, 15A18, 65F15, 93D05
- DOI: https://doi.org/10.1090/S0002-9904-1977-14295-X
- MathSciNet review: 0422309