Skip to main content

Part of the book series: Numerical Methods and Algorithms ((NUAL,volume 1))

  • 449 Accesses

Abstract

In this Chapter, we will present some methods for the numerical inversion of the Laplace transform. We will also discuss the inversion of the z-transform which can be considered as the discrete analog of the Laplace transform.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. C. Brezinski, Algorithmes d’Accélération de la Convergence. Etude Numérique, Editions Technip, Paris, 1978.

    MATH  Google Scholar 

  2. C. Brezinski, M. Redivo Zaglia, Extrapolation Methods. Theory and Practice, North-Holland, Amsterdam, 1991.

    MATH  Google Scholar 

  3. A. Bultheel, M. van Barel, Padé techniques for model reduction in linear system theory: a survey, J. Comput. Appl. Math., 14 (1986) 401–438.

    Article  MathSciNet  Google Scholar 

  4. I. Longman, On the generation of rational function approximations for Laplace transform inversion with an application to viscoelasticity, SIAM J. Appl. Math., 24 (1973) 429–440.

    Article  MATH  Google Scholar 

  5. I.M. Longman, M. Sharir, Laplace transform inversion of rational functions, Geophys. J. R. Astrom. Soc., 25 (1971) 299–305.

    MATH  Google Scholar 

  6. M.F. Marziani, Convergence of a class of Borel-Padé type approximants, Nuovo Cimento, 99B (1987) 145–154.

    MathSciNet  Google Scholar 

  7. G. de Prony, Essai expérimental et analytique, J. Ec. Polytechnique, 1 (2) (1795) 24–76.

    Google Scholar 

  8. A. Sidi, The Padé table and its connection with some weak exponential function approximation to Laplace transform inversion, in Padé Approximation and its Applications. Amsterdam 1980, M.G. de Bruin and H. van Rossum eds, LNM vol. 888, Springer-Verlag, Berlin, 1981, pp. 352–362.

    Chapter  Google Scholar 

  9. R. Vich, Z-Transform. Theory and Applications, Reidel, Dordrecht, 1987.

    MATH  Google Scholar 

  10. L. Weiss, R.N. McDonough, Prony’s method, z-transforms, and Padé approximations, SIAM Rev., 5 (1963) 145–149.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Kluwer Academic Publishers

About this chapter

Cite this chapter

Brezinski, C. (2002). Transform Inversion. In: Brezinski, C. (eds) Computational Aspects of Linear Control. Numerical Methods and Algorithms, vol 1. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0261-2_5

Download citation

  • DOI: https://doi.org/10.1007/978-1-4613-0261-2_5

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4020-0711-8

  • Online ISBN: 978-1-4613-0261-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics