Abstract
In this paper, a kind of inverse eigenvalue problem which is the reconstruction of real symmetric five-diagonal matrix by there different eigenpairs is proposed. Given there distinguished eigenpairs, using the special computational relationship of Jacobi matrix and symmetric five-diagonal matrix, the solvability of the problem is discussed, and the sufficient and necessary conditions for the existence of a solution of this problem, as well as the analytic formula of this solution, are derived. Furthermore, to prove the theory, an appropriate numerical experiment is given by programming.
Supported by the Natural Science foundation of Hebei Province of China (No. A2010000905).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Dai, H.: Inverse Eigenvalue Problems for Jacobian and Symmetric Trididagonal Matrices. J. Numerical Mathematics A Journal of Chinese Universities 12(1), 1–13 (1990)
Hu, X.Y., Zhou, X.Z.: Inverse Eigenvalue Problems for Tridiagonal Symmetric Matrices. J. Journal on Numerical Methods and Computer Applications 17(2), 150–156 (1996)
Liao, A.P., Zhang, L., Hu, X.Y.: The Conditions of Existing a Unique Solution for Inverse Eigenproblems of Tridiagonal Symmetric Matrices. J. Journal on Numerical Methods and Computer Applications 21(2), 102–111 (2000)
Liao, A.P., Bai, Z.Z.: On the Construction of Positive Definite Jacobian Matrix from Two Eignpairs. J. Journal of Numerical Methods and Computer Applications 23(2), 131–138 (2002)
Li, Z.Z.: On the Construction of Positive Definite Jacobian Matrix from Therer Eignpairs. J. Acta Mathematicae Applicatae Sinica 28(2), 333–340 (2005)
Zhou, X.Z., Hu, X.Y.: The Real Symmetric Five-Diagonal Matrix and Inverse Eigenproblems for It. J. Journal of Hunan University 23(1), 9–14 (1996)
Wang, Z.S.: Inverse Eigenvalue Problem for Real Symmetric Five-Diagonal Matrix. J. Numerical Mathematics A Journal of Chinese Universities 4, 366–376 (2002)
Sun, H.M., Zhao, C.S.: An Algorithm and Application For Inverse Eigenvalue Problem of 5-Diagonal Matrix. J. Chinese Journal of Computational Physics 14(4,5), 631–634 (1997)
Wang, Z.S.: Inverse eigenvalue problems for real symmetric banded matrix. J. Applied Mathematics A Journal of Chinese Universities 19(4), 451–459 (2004)
Cai, Q., Fang, F.: The Conditions for the Solvability of Inverse Problems of Two Matrixes. J. Nanjing Audit University Journal 2(4), 66–69 (2005)
Cai, Q., Gong, W.Q., Sun, A.M.: Inverse Eigenvalue Problem for Real Symetric Five-diagonal Matrix. J. College Mathematics 21(6), 66–70 (2005)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Feng, L., Li, P., Gong, D., Li, L., Yang, A., Qu, J. (2010). Inverse Eigenvalue Problem for Real Symmetric Five-Diagonal Matrix. In: Zhu, R., Zhang, Y., Liu, B., Liu, C. (eds) Information Computing and Applications. ICICA 2010. Communications in Computer and Information Science, vol 106. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16339-5_36
Download citation
DOI: https://doi.org/10.1007/978-3-642-16339-5_36
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-16338-8
Online ISBN: 978-3-642-16339-5
eBook Packages: Computer ScienceComputer Science (R0)