Matrix Randomization Methods

  • Roberto Tempo
  • Giuseppe Calafiore
  • Fabrizio Dabbene
Part of the Communications and Control Engineering book series (CCE)

Abstract

This chapter presents algorithms for uniform matrix sample generation in norm-bounded sets. First, we discuss the simple case of matrix sampling in sets defined by p Hilbert–Schmidt norm, which reduces to the vector p norm randomization problem. Subsequently, we present an efficient solution to the problem of uniform generation in sets defined by the spectral norm.

Keywords

Manifold 

References

  1. 4.
    Abramowitz M, Stegun IA (eds) (1970) Handbook of mathematical functions. Dover, New York Google Scholar
  2. 81.
    Calafiore G, Dabbene F (2002) A probabilistic framework for problems with real structured uncertainty in systems and control. Automatica 38:1265–1276 MathSciNetMATHCrossRefGoogle Scholar
  3. 83.
    Calafiore G, Dabbene F, Tempo R (2000) Randomized algorithms for probabilistic robustness with real and complex structured uncertainty. IEEE Trans Autom Control 45:2218–2235 MathSciNetMATHCrossRefGoogle Scholar
  4. 126.
    de Bruijn NG (1955) On some multiple integrals involving determinants. J Indian Math Soc 19:133–151 MathSciNetMATHGoogle Scholar
  5. 210.
    Hua LK (1979) Harmonic analysis of functions of several complex variables in the classical domains. American Mathematical Society, Providence MATHGoogle Scholar
  6. 281.
    Mehta ML (1991) Random matrices. Academic Press, Boston MATHGoogle Scholar
  7. 369.
    Stewart GW (1980) The efficient generation of random orthogonal matrices with an application to condition estimators. SIAM J Numer Anal 17:403–409 MathSciNetMATHCrossRefGoogle Scholar
  8. 403.
    Vein R, Dale P (1999) Determinants and their applications in mathematical physics. Springer, New York MATHGoogle Scholar
  9. 423.
    Zhou T, Feng C (2006) Uniform sample generation from contractive block Toeplitz matrices. IEEE Trans Autom Control 51:1559–1565 MathSciNetCrossRefGoogle Scholar
  10. 424.
    Zyczkowski K, Kus M (1994) Random unitary matrices. J Phys 27(A):4235–4245 MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag London 2013

Authors and Affiliations

  • Roberto Tempo
    • 1
  • Giuseppe Calafiore
    • 2
  • Fabrizio Dabbene
    • 1
  1. 1.CNR - IEIITPolitecnico di TorinoTurinItaly
  2. 2.Dip. Automatica e InformaticaPolitecnico di TorinoTurinItaly

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