Fast Algorithm for the Inverse Matrices of Adding Element Tridiagonal Periodic Matrices in Signal Processing

Article Preview

Abstract:

Adding element tridiagonal matrices play a very important role in the theory and practical applications, such as the boundary value problems by finite difference methods, interpolation by cubic splines, three-term difference equations and so on. In this paper, we give a fast algorithm for the Inverse Matrices of periodic adding element tridiagonal matrices.

You might also be interested in these eBooks

Info:

Periodical:

Advanced Materials Research (Volumes 121-122)

Pages:

682-686

Citation:

Online since:

June 2010

Export:

Price:

Permissions CCC:

Permissions PLS:

Сopyright:

© 2010 Trans Tech Publications Ltd. All Rights Reserved

Share:

Citation:

[1] P.N. Shivakumar, Ji Chuanxiang, Upper and lower bounds for inverse elements of finite and infinite tridiagonal matrices, Linear Algebra Appl., Vol. 247(1996) , pp.297-316.

DOI: 10.1016/0024-3795(95)00113-1

Google Scholar

[2] YUAN Zhi-jie, XU Zhong, Upper Bounds for Inverse Elements of Strictly Diagonally Dominant Periodic Tridiagonal Matrices, Chinese Journal of Engineering Mathematics, Vol. 21(2004) , pp.67-72.

Google Scholar

[3] R. Peluso,T. Politi, Some improvements for two-sided bounds on the inverse of diagonally dominant tridiagonal matrices, Linear. Algebr. Appl., Vol. 330(2001) , pp.1-14.

DOI: 10.1016/s0024-3795(01)00254-3

Google Scholar

[4] XiaoQin Liu, TingZhu Huang, Ying-Ding Fu, Estimates for the inverse elements of tridiagonal matrices, Applied Mathematics Letters, Vol. 19(2006)4, pp.590-598.

DOI: 10.1016/j.aml.2005.08.009

Google Scholar

[5] D. Kershaw, Inequalities on the elements of the inverse of a certain tridiagonal matrix, Math. Comput. Vol. 24(1970), pp.155-158.

DOI: 10.1090/s0025-5718-1970-0258260-5

Google Scholar

[6] R. Nabben , Two-sided bounds on the inverse of diagonally dominant tridiagonal matrices, Linear Algebr. Appl., Vol. 287(1999) , pp.289-305.

DOI: 10.1016/s0024-3795(98)10146-5

Google Scholar

[7] YANG Chuan-sheng, YANG Shang-jun, Closure Properties of Inverse M-matrices under Hadamard Product, Journal of Anhui University(Natural Sciences), Vol. 4(2000) , pp.15-20.

Google Scholar

[8] Zhong Xiu, Kaiyuan Zhang, Quan Lu, Fast algorithm for Toeplitz matrix, Northwestern Polytechnical University Press(1999).

Google Scholar

[9] LOU Xu-yang CUI Bao-tong, Exponential dissipativity of Cohen-Grossberg neural networks with mixed delays and reaction-diffusion terms, Vol. 4(2008), pp.619-922.

Google Scholar

[10] GUO Xi-juan, JI Nai-hua, YAO Hui-ping, The Judgement and Parallel Algorithm for Inverse M-matrixes , Journal of Beihua University, Vol. 45(2004), pp.97-103.

Google Scholar

[11] YANG zhong-yuan , FU Ying-ding , and HuANG Ting-zhu, Some Properties of InverseM-Matrices and Their Applications, Joumal of UEST of China Vol. 34(2005), pp.713-716.

Google Scholar

[12] HAN Yin, The Property and Judgment of Inverse M-Matrixes, Journal of Huzhou Teachers College, Vol. 30(2008), pp.10-12.

Google Scholar

[13] You Zhaoyong, Nonsingular M-matrix[M]. Wuhan: Huazhong University of Science and Technology Publishing House, (1983).

Google Scholar

[14] Zhaolin Jiang, Non singularity on scaled factor circulant matrices, Journal of Baoji College of Arts and Science (!atural Science, 23 (2003) 5-7.

Google Scholar

[15] Hongkui Li, Xueting Liu and Wenling Zhao, Nonsingularity on Scaled Factor Circulant Matrices, International Journal of Algebra, Vol. 2, 2008, no. 18, 889 - 893.

Google Scholar

[16] Zhaolin Jiang, Non singularity on r-circulant matrices, Mathematics in Practice and Theory, 2(1995) 52-58.

Google Scholar

[17] Deng Yihua, Problem of Cyclic Matrix Inversion, Journal of Hengyang !ormal University, 3(1995) 31-33.

Google Scholar

[18] Jiang Jiaqing, Two Simple Methods of Finding Inverse Matrix of Cyclic Matrix, Journal of Jiangxi Institute of Education(Comprehensive) , 3(2008) 5-6.

Google Scholar

[19] Zhaolin Jiang, Liu Sanyang, The Fast Algorithm for Finding the Inverse and Generalized Inverse of Permutation Factor Circulant Matrix, !umerical Mathematics A Journal of Chinese Universities, 03(2003)227-234(in Chinese).

Google Scholar

[20] R.E. Cline, R.J. Plemmons and G. Worm, Generalized inverses of certain Toeplitz matrices, Linear Algebra and Its Applications, 8(1974), 25-33.

DOI: 10.1016/0024-3795(74)90004-4

Google Scholar

[21] Zhaolin Jiang, Zhou Zhangxin, Circulant Matrices, Chengdu Technology University Publishing Company, Chengdu, (1999).

Google Scholar

[22] Shen Guangxing, The Time Complexity of r-circulant Syestems [J], Journal Mathematical Research and Exposition, 4(1992), 595-598.

Google Scholar