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.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
A. Bloch and P. Crouch, Optimal control and geodesic flows, Systems & Control Letters, 28, N. 3 (1996), 65–72.
J. R. Cardoso and F. Silva Leite, Theoretical and numerical considerations about logarithms of matrices. Submitted in 1999.
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.
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.
G. Golub and C. Van Loan, Matrix Computations. Johns Hopkins Univ. Press, 3rd ed., Baltimore, MD, USA, 1996.
-N. J. Higham, Computing real square roots of a real matrix, Linear Algebra and its Applications, 88/89, (1987), 405–430.
N. J. Higham, Stable iterations for the matrix square root, Numerical Algorithms, 15, (1997), 227–242.
N. J. Higham, A new sqrtm for Matlab, Numerical Analysis Report, 336, (1999), University of Manchester.
R. A. Horn and C. R. Johnson, Topics in Matrix Analysis. Cambridge University Press, 1994.
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.
C. Kenney and A. J. Laub, Condition estimates for matrix functions, SIAM Journal on Matrix Analysis and Applications, 10, (1989), 191–209.
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.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights 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