Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
Springer Nature Link
Log in

Computing the Inverse Matrix Hyperbolic Sine

  • Conference paper
  • First Online:
Numerical Analysis and Its Applications (NAA 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1988))

Included in the following conference series:

Abstract

We give necessary and sufficient conditions for solvability of the matrix equation sinhX = A in the complex and real cases and present some algorithms for computing one of these solutions. The numerical features of the algorithms are analysed along with some numerical tests.

Work supported in part by ISR and research network contract ERB FMRXCT- 970137.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 109.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 139.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. A. Bloch and P. Crouch, Optimal control and geodesic flows, Systems & Control Letters, 28, N. 3 (1996), 65–72.

    Article  MATH  MathSciNet  Google Scholar 

  2. J. R. Cardoso and F. Silva Leite, Theoretical and numerical considerations about logarithms of matrices. Submitted in 1999.

    Google Scholar 

  3. L. Dieci, B. Morini and A. Papini, Computational techniques for real logarithms of matrices, SIAM Journal on Matrix Analysis and Applications, 17, N. 3, (1996), 570–593.

    Article  MATH  MathSciNet  Google Scholar 

  4. L. Dieci, B. Morini, A. Papini and A. Pasquali, On real logarithms of nearby matrices and structured matrix interpolation, Appl. Numer. Math., 29 (1999), 145–165.

    Article  MATH  MathSciNet  Google Scholar 

  5. G. Golub and C. Van Loan, Matrix Computations. Johns Hopkins Univ. Press, 3rd ed., Baltimore, MD, USA, 1996.

    Google Scholar 

  6. -N. J. Higham, Computing real square roots of a real matrix, Linear Algebra and its Applications, 88/89, (1987), 405–430.

    Article  MathSciNet  Google Scholar 

  7. N. J. Higham, Stable iterations for the matrix square root, Numerical Algorithms, 15, (1997), 227–242.

    Article  MATH  MathSciNet  Google Scholar 

  8. N. J. Higham, A new sqrtm for Matlab, Numerical Analysis Report, 336, (1999), University of Manchester.

    Google Scholar 

  9. R. A. Horn and C. R. Johnson, Topics in Matrix Analysis. Cambridge University Press, 1994.

    Google Scholar 

  10. C. Kenney and A. J. Laub, Padé error estimates for the logarithm of a matrix, International Journal of Control, 50, N. 3, (1989), 707–730.

    Article  MATH  MathSciNet  Google Scholar 

  11. C. Kenney and A. J. Laub, Condition estimates for matrix functions, SIAM Journal on Matrix Analysis and Applications, 10, (1989), 191–209.

    Article  MATH  MathSciNet  Google Scholar 

  12. C. Kenney and A. J. Laub, A Schur-Frechet algorithm for computing the logarithm and exponential of a matrix, SIAM Journal on Matrix Analysis and Applications, 19, N. 3, (1998), 640–663.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Instituto Superior de Engenharia de Coimbra, Quinta da Nora, 3030, Coimbra, Portugal

    J. R. Cardoso

  2. Departamento de Matemática, Universidade de Coimbra, 3000, Coimbra, Portugal

    F. Silva Leite

Authors
  1. J. R. Cardoso
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. F. Silva Leite
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Rousse, 7000, Rousse, Bulgaria

    Lubin Vulkov  & Plamen Yalamov  & 

  2. UNI-C,Danish Computing Center for Research and Education, DTU,Building 304, 2800, Lyngby, Denmark

    Jerzy Waśniewski

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Cardoso, J.R., Silva Leite, F. (2001). Computing the Inverse Matrix Hyperbolic Sine. In: Vulkov, L., Yalamov, P., Waśniewski, J. (eds) Numerical Analysis and Its Applications. NAA 2000. Lecture Notes in Computer Science, vol 1988. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45262-1_20

Download citation

  • DOI: https://doi.org/10.1007/3-540-45262-1_20

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41814-6

  • Online ISBN: 978-3-540-45262-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation