PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
2014 | 2 | 1 |
Tytuł artykułu

Singular M-matrices which may not have a nonnegative generalized inverse

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A matrix A ∈ ℝn×n is a GM-matrix if A = sI − B, where 0 < ρ(B) ≤ s and B ∈WPFn i.e., both B and Bt have ρ(B) as their eigenvalues and their corresponding eigenvector is entry wise nonnegative. In this article, we consider a generalization of a subclass of GM-matrices having a nonnegative core nilpotent decomposition and prove a characterization result for such matrices. Also, we study various notions of splitting of matrices from this new class and obtain sufficient conditions for their convergence.
Wydawca
Czasopismo
Rocznik
Tom
2
Numer
1
Opis fizyczny
Daty
otrzymano
2014-03-31
zaakceptowano
2014-09-04
online
2014-11-07
Twórcy
  • Ramanujan Institute of Advanced Study in Mathematics, University of Madras,
    Chennai,- 600005, India
  • Ramanujan Institute of Advanced Study in Mathematics, University of Madras,
    Chennai,- 600005, India
  • Department of Mathematics, Indian Institute of Technology Madras, Chennai - 600 036, India
Bibliografia
  • [1] A. Ben-Israel and T.N.E. Greville, Generalized Inverses: Theory and applications: Springer-Verlag, New York, 2003.
  • [2] Agrawal N. Sushma, K.Premakumari and K.C. Sivakumar, Extensions of Perron-Frobenius splittings and relationships withnonnegative Moore-Penrose inverses, Lin. Multilinear Alg., DOI: 10. 1080/03081087.2013.840616[Crossref]
  • [3] A. Berman and R.J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, SIAM, Philadelphia, 1994.
  • [4] A. Berman and R.J. Plemmons, Cones and iterative methods for best least squares solutions of linear systems, SIAM J. Numer.Anal., 11 (1974), 145-154.[Crossref]
  • [5] S.L. Campbell and C.D. Meyer, Jr., Generalized Inverses of Linear Transformations, Dover, Inc., New York, 1991.
  • [6] A. Elhashah and D.B. Szyld, Perron-Frobenius properties of general matrices, Research Report 07-01-10, Department ofMathematics, Temple University, Revised, November 2007.
  • [7] A. Elhashah and D.B. Szyld, Generalization of M-matrices which may not have a nonnegative inverse, Lin. Alg. Appl., 429(2008), 2435–2450.
  • [8] A. Elhashah and D.B. Szyld, Two characterizations of matrices with Perron-Frobenius property, Num. Linear Alg. App., (2009),1–6.
  • [9] F. Chatelin, Eigenvalues of Matrices, John Wiley & Sons, Philadelphia, USA, 1993.
  • [10] L. Jena, D. Mishra and S. Pani, Convergene and comparison theorem for single and double decompositions of rectangularmatrices, Calcolo, 51 (2014), 141-149.[WoS]
  • [11] C.R. Johnson and P. Tarazaga, On matrices with Perron-Frobenius properties and some negative entries, Positivity, 8 (2004),327-338.[Crossref]
  • [12] H.T. Le and J.J. McDonald, Inverses of M-type matrices created with irreducible eventually nonnegative matrices, Lin. Alg.Appl., 419 (2006), 668-674.
  • [13] D. Mishra and K.C. Sivakumar, On splitting of matrices and nonnegative generalized inverses, Oper. Matrices, 6 (2012),85-95.[Crossref]
  • [14] D.Mishra, Nonnegative splittings for rectangular matrices, Computers and Mathematics with Applications, 67 (2014), 136-144.[WoS]
  • [15] D. Noutsos, On Perron-Frobenius property of matrices having some negative entries, Lin. Alg. Appl., 412 (2006), 132–153.
  • [16] D.D. Olesky, M.J. Tsatsomeros and P.Van Den Driessche, Mv-matrces: A Generalization of M-matrices based on eventuallynonnegative matrices, Elec. J. Linear Algebra, 18 (2008), 339-351.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_spma-2014-0017
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.