Advertisement

Approximation to Linear Algebraic Transition System

  • Zhiwei Zhang
  • Jin-Zhao Wu
  • Hao Yang
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 304)

Abstract

We analyze the linear algebraic transition system (LATS) using algebraic theory. For transiting computing of linear algebraic transition system (LATS), we propose a concept of k-times maximum approximate transiting about (B, ε) which B is used to approximating compute for powers of the matrix A of the LATS. ε is maximum absolute error. This method can improve computational speed and conserve memory of computer program which can be modeled by the algebraic transition system. Further more, the theory and its function are verified by a practical example.

Keywords

K-times maximum approximate transiting linear algebraic transition system powers of the matrix 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Hochbruck, M.: On Krylov Subspace Approximations to the Matrix Exponential Operator. SIAM Journal on Numerical Analysis, 1911–1925 (1994)Google Scholar
  2. 2.
    Frieze, A., Kanna, R.: Fast Monte-Carlo Algorithms For Finding Low-Rank Approximations. Journal of the ACM (JACM), 1025–1041 (2004)Google Scholar
  3. 3.
    Drineas, P., Kannan, R., Mahoney, M.W.: Fast Monte Carlo Algorithms for Matrices III: Computing a Compressed Approximate Matrix Decomposition. SIAM Journal on Computing, 184–206 (2006)Google Scholar
  4. 4.
    Drineas, P., Kannan, R.: Fast Monte Carlo Algorithms for Matrices I: Approximating Matrix Multiplication. SIAM Journal on Computing, 132–157 (2006)Google Scholar
  5. 5.
    Van, J., Eshof, D.: Preconditioning Lanczos Approximations To The Matrix Exponential. SIAM Journal on Scientific Computing, 1438–1457 (2006)Google Scholar
  6. 6.
    Moret, I.: RD-Rational Approximations of The Matrix Exponential. BIT Numerical Mathematics, 595–615 (2004)Google Scholar
  7. 7.
    Zanna, A.: Generalized Polar Decompositions For The Approximation of The Matrix Exponential. SIAM Journal on Matrix Analysis and Applications 23, 840–862 (2002)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Manna, Z., Pnueli, A.: Temporal Verification of Reactive Systems: Safety. Springer, New York (1995)CrossRefGoogle Scholar
  9. 9.
    Meyer, C.D.: Convergent Powers of a Matrix with Applications to Iterative Methods for Singular Linear Systems. SIAM Journal on Numerical Analysis, 699–712 (1977)Google Scholar
  10. 10.
    Thomason, M.G.: Convergence of Powers of a Fuzzy Matrix. Journal of Mathematical Analysis and Applications, 476–480 (1977)Google Scholar
  11. 11.
    Hashimoto, H.: Convergence Of Powers Of A Fuzzy Transitive Matrix. Fuzzy Sets and Systems, 153–160 (1983)Google Scholar
  12. 12.
    Sriram, S.: Non-linear Loop Invariant Generation using GROBNER Bases. ACM SIGPLAN Notices, 318–329 (2004)Google Scholar
  13. 13.
    Stewart, G.W.: Matrix Perturbation Theory (1990)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Zhiwei Zhang
    • 1
  • Jin-Zhao Wu
    • 2
    • 3
  • Hao Yang
    • 1
  1. 1.Chengdu Institute of Computer ApplicationChinese Academy of SciencesChengduChina
  2. 2.Guangxi Key Laboratory of Hybrid Computational and IC Design AnalysisGuangxi University for NationalitiesNanningChina
  3. 3.School of Computer and Information TechnologyBeijing Jiaotong UniversityBeijingChina

Personalised recommendations