Doubly Stochastic Interval Matrices

Doubly Stochastic Interval Matrices

Interval matrices have many applications in intelligent engineering problems such as robotics in computer science. In this paper, we will first describe the concepts of interval matrices. Next, we will introduce a new class of interval matrices, namely, doubly stochastic interval matrices. Finally, we will present some properties of this new class of matrices.

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  • [1] H. R. Arndt, On Interval Systems [x] = [A][x] + [b] and the Powers of Interval Matrices in Complex Interval Arithmetics, Reliable Computing, (2007), 13, 245-259.
  • [2] H. Atrianfar, M. Haeri, Average Consensus in Networks of Dynamic Multi-agents with Switching Topology: Infinite Matrix Products, ISA Transactions, (2012), 51(4), 522-530.
  • [3] F. Bullo, J. Cortes, S. Martinez, Distributed Control of Robotic Networks, Applied Mathematics Series, Princeton University Press, (2009).
  • [4] S. Hwang, S. Pyo, The Inverse Eigenvalue Problem for Symmetric Doubly Stochastic Matrices, Linear Algebra and Applied Mathematics, (2004), 379, 77-83.
  • [5] L. Jaulin, M. Kieffer, O. Didrit, E. Walter, Applied Interval Analysis, Springer-Verlag London, Berlin, Heidelberg, (2001).
  • [6] J. P. Merlet, Interval Analysis and Robotics, Springer Tracts in Advanced Robotics, (2011), 66, 147-156.
  • [7] H. Minc, Nonnegative Matrices, A Wiley-Interscience Publication, New York, (1988).
  • [8] R. E. Moore, Interval Analysis, Prentice-Hall, Englewood Cliffs, N.J., (1966).
  • [9] A. Neumaier, Interval Methods for System of Equations, Cambridg University press, (1990).
  • [10] Rohn J., A Handbook of Results on Interval Linear Problems, (2005), URL: http://www.cs.cas.cz/rohn/handbook/.