Advanced Search
Article Contents
Article Contents

Index-range monotonicity and index-proper splittings of matrices

Abstract Related Papers Cited by
  • Index-range monotonicity is proposed, and some characterizations of this notion are obtained. Then different convergence and comparison theorems are presented using several new subclasses of index-proper splittings.
    Mathematics Subject Classification: Primary: 15A09, 65F15, 65F20.


    \begin{equation} \\ \end{equation}
  • [1]

    A. Ben-Israel and T. N. E. Greville, "Generalized Inverses, Theory and Applications," Springer-Verlag, New York, 2003.


    A. Berman and R. J. Plemmons, Cones and iterative methods for best square least squares solutions of linear systems, SIAM J. Numer. Anal., 11 (1974), 145-154.doi: 10.1137/0711015.


    A. Berman and R. J. Plemmons, Monotonicity and the generalized inverse, SIAM J. Appl. Math., 22 (1972), 155-161.doi: 10.1137/0122018.


    A. Berman and R. J. Plemmons, Matrix group monotonicity, Proceedings of the American Mathematical Society, 46 (1974), 355-359.doi: 10.1090/S0002-9939-1974-0352116-0.


    A. Berman and R. J. Plemmons, Eight types of matrix monotonicity, Linear Algebra and Appl., 13 (1976), 115-123.doi: 10.1016/0024-3795(76)90049-5.


    G. Chen and X. Chen, A new splitting for singular linear system and Drazin inverse, J. East China Norm. Univ. Natur. sci. Ed., 3 (1996), 12-18.


    L. Collatz, Aufgaben monotoner Art, Arch. Math., 3 (1952), 366-376.doi: 10.1007/BF01899376.


    L. Jena and D. Mishra, Comparison theorems for Brow and Bran-splittings of matrices, Linear and Multilinear Algebra, 61 (2013), 35-48.doi: 10.1080/03081087.2012.661426.


    L. Jena and D. Mishra, BD-splittings of matrices, Linear Algebra and Appl., 437 (2012), 1162-1173.doi: 10.1016/j.laa.2012.04.009.


    L. Jena and S. PaniInterval Drazin monotonicity of matrices, Revised version submitted to Vietnam Journal of Mathematics.


    M. A. Krasnosel'skij, A. Je. Lifshits and A. V. Sobolev, "Positive Linear Systems," Heldermann Verlag, Berlin, 1989.


    D. Mishra, "Least Elements, Matrix Splittings and Nonnegative Generalized Inverses," PhD Thesis, IIT Madras, 2012.


    D. Mishra and K. C. Sivakumar, Generalizations of matrix monotonicity and their relationships with certain subclasses of proper splittings, Linear Algebra Appl., 436 (2012), 2604-2614.doi: 10.1016/j.laa.2011.11.016.


    J. E. Peris, A new characterization of inverse-positive matrices, Linear Algebra Appl., 154/156 (1991), 45-58.doi: 10.1016/0024-3795(91)90372-4.


    J. E. Peris and B. Subizas, A characterization of weak-monotone matrices, Linear Algebra Appl., 166 (1992), 167-184.doi: 10.1016/0024-3795(92)90275-F.


    W. C. Pye, Nonnegative Drazin inverses, Linear Algebra Appl., 30 (1980), 149-153.doi: 10.1016/0024-3795(80)90190-1.


    A. Schrijver, "Theory of Linear and Integer Programming," John Wiley & Sons Ltd., Chichester, 1986.


    Y. Song, Comparisons of nonnegative splittings of matrices, Linear Algebra Appl., 154-156 (1991), 453-455.doi: 10.1016/0024-3795(91)90388-D.


    R. S. Varga, "Matrix Iterative Analysis," Springer-Verlag, Berlin, 2000.doi: 10.1007/978-3-642-05156-2.


    Y. Wei, Index splitting for the Drazin inverse and the singular linear system, Appl. Math. Comput., 95 (1998), 115-124.doi: 10.1016/S0096-3003(97)10098-4.


    Z. I. Woźnicki, Matrix splitting principles, Novi Sad J. Math., 28 (1998), 197-209.


    Z. I. Woźnicki, Nonnegative splitting theory, Japan J. Industr. Appl. Math., 11 (1994), 289-342.doi: 10.1007/BF03167226.

  • 加载中

Article Metrics

HTML views() PDF downloads(107) Cited by(0)

Access History

Other Articles By Authors



    DownLoad:  Full-Size Img  PowerPoint