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Czasopismo

2016 | 4 | 1 | 181-188

Tytuł artykułu

On a criterion of D-stability for P-matrices

Autorzy

Treść / Zawartość

Warianty tytułu

Języki publikacji

EN

Abstrakty

EN
In this paper, we study positive stability and D-stability of P-matrices.We introduce the property of Dθ-stability, i.e., the stability with respect to a given order θ. For an n × n P-matrix A, we prove a new criterion of D-stability and Dθ-stability, based on the properties of matrix scalings.

Wydawca

Czasopismo

Rocznik

Tom

4

Numer

1

Strony

181-188

Opis fizyczny

Daty

otrzymano
2015-10-23
zaakceptowano
2016-03-22
online
2016-04-11

Twórcy

  • Shanghai Jiao Tong University, Department of Mathematics, Dong Chuan Road 800, 200240 Shanghai, China

Bibliografia

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  • [3] A. Berman, R.J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, Academic Press, New York, 1979.
  • [4] B. Cain, Real, 3 × 3, D-stable matrices, J. Res. Nat. Bur. Standards Sect. B, 80B (1976), 75–77.
  • [5] D. Carlson, A class of positive stable matrices, J. Res. Nat. Bur. Standards Sect. B, 78B (1974), pp. 1–2.
  • [6] M. Fiedler and V. Pták, On matrices with non-positive off-diagonal elements and positive principal minors, Czech. Math. J., 22 (87) (1962), pp. 382–400.
  • [7] M.E. Fisher and A.T. Fuller, On the stabilization of matrices and the convergence of linear iterative processes, Proc. Cambridge Philos. Soc., 54 (1958), pp. 417–425.
  • [8] I.M. Glazman and Yu.I. Liubich, Finite-Dimensional Linear Analysis: A Systematic Presentation in Problem Form, MIT Press, 1974.
  • [9] D.A. Grundy, C.R. Johnson, D.D. Olesky and P. van den Driessche, Products of M-matrices and nested sequences of principal minors, ELA, 16 (2007), pp. 380–388.
  • [10] D. Hershkowitz, On the spectra of matrices having nonnegative sums of principal minors, Linear Algebra Appl., 55 (1983), pp. 81–86. [Crossref]
  • [11] D. Hershkowitz and C.R. Johnson, Spectra of matrices with P-matrix powers, Linear Algebra Appl., 80 (1986), pp. 159–171. [Crossref]
  • [12] D. Hershkowitz and N. Keller, Positivity of principal minors, sign symmetry and stability, Linear Algebra Appl., 364 (2003), pp. 105–124. [Crossref]
  • [13] G.V. Kanovei and D.O. Logofet, D-stability of 4-by-4 matrices, Comput. Math. Math. Phys., 38 (1998), pp. 1369–1374.
  • [14] D.O. Logofet, Stronger-than-Lyapunov notions of matrix stability, or how"flowers" help solve problems in mathematical ecology, Linear Algebra Appl. 398 (2005), 75-100.
  • [15] C.R. Johnson, Sufficient conditions for D-stability, Journal of Economic Theory 9 (1974), 53-62. [Crossref]
  • [16] A. Pinkus, Totally positive matrices, Cambridge University Press, 2010.
  • [17] J.P. Quirk, R. Ruppert, Qualitative economics and the stability of equilibrium, Rev. Econom. Studies 32 (1965), 311-326. [Crossref]
  • [18] A.K. Tang, A. Simsek, A. Ozdaglar and D. Acemoglu, On the stability of P-matrices, Linear Algebra Appl., 426 (2007), 22–32. [Crossref]
  • [19] M. Tsatsomeros, Generating and detecting matrices with positive principal minors, Asian Information-Science-Life, 1 (2002), p. 115–132.

Typ dokumentu

Bibliografia

Identyfikatory

Identyfikator YADDA

bwmeta1.element.doi-10_1515_spma-2016-0017
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