A Method for Computing Logarithms of K-Circulant Matrices

Article Preview

Abstract:

In this paper, we present an efficient algorithm for computing the logarithms of k-circulant matrices. And then we prove that nonsingular k-circulant matrices always has infinitely many k-circulant logarithms.

You might also be interested in these eBooks

Info:

Periodical:

Pages:

661-664

Citation:

Online since:

July 2014

Authors:

Export:

Price:

Permissions CCC:

Permissions PLS:

Сopyright:

© 2014 Trans Tech Publications Ltd. All Rights Reserved

Share:

Citation:

* - Corresponding Author

[1] P. J. Davis: Circulant Matrices, second ed., Chelsea Publishing, New York, (1994).

Google Scholar

[2] R. M. Gray: Toeplitz and circulant matrices: a review, Stanford University Press, (2000).

Google Scholar

[3] A. Berman, R. Plemmons: Nonnegative Matrices in the Mathematical Sciences, Academic Press, New York, (1979).

Google Scholar

[4] Y. Mei: Computing the square roots of generalized circulant matrices, Journal of Applied Mathematics, Vol. 2012, 1-15.

Google Scholar

[5] C. B. Lu and C.Q. Gu: The computation of the square roots of circulant matrices, Applied Mathematics and Computation, Vol. 217(2011), 6819-6829.

DOI: 10.1016/j.amc.2011.01.018

Google Scholar

[6] C. B. Lu and C.Q. Gu: The computation of the inverse of block-wise centrosymmetric matrices, Publicationes Mathematicae Debrecen, Vol. 82/2(2013), 379-397.

DOI: 10.5486/pmd.2013.5329

Google Scholar

[7] C. B. Lu and D.S. Yu: On the approximation of functions by Fourier Stieltjes Series, Bulletin of the Belgian Mathematical Society – Simon Stevin, 20 (2013), 667–674.

DOI: 10.36045/bbms/1382448187

Google Scholar

[8] C. B. Lu: The properties and iterative algorithms of circulant matrices, Journal of Computational Analysis and Applications, Vol. 16, No. 3(2014), 592-605.

Google Scholar

[9] C. B. Lu: On the logarithms of circulant matrices, Journal of Computational Analysis and Applications, Vol. 15, No. 3(2013), 402-412.

Google Scholar

[10] C. S. Kenney, A. J. Laub: Condition estimates for matrix functions. SIAM J. Matrix Anal. Appl., 10(2)(1989), 191-209.

DOI: 10.1137/0610014

Google Scholar

[11] S. H. Cheng, N.J. Higham, C. S. Kenney, A. J. Laub: Approximating the logarithm of a matrix to specified accuracy. SIAM J. Matrix Anal. Appl., 22(4)(2001), 1112-1125.

DOI: 10.1137/s0895479899364015

Google Scholar