Estimates for the Lower Bounds on the Inverse Elements of Strictly Diagonally Dominant Tridiagonal Matrices in Signal Processing

Abstract:

In the theory and practical applications, tridiagonal matrices play a very important role. In this paper, Motivated by the references, especially [2], we give the estimates for the lower bounds on the inverse elements of strictly diagonally dominant tridiagonal matrices.

• Periodical: Advanced Materials Research (Volumes 121-122)
• Pages: 929-933
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.121-122.929
• Online since: June 2010
• Authors: Chuan Dai Dong
• Keywords: Inverse Matrix, Lower Bound, Signal Processing, Strictly Diagonally Dominant, Tridiagonal Matrices

References

[1] Huihua Zhu, The Criteria Of Specific Shape Inverse M − Matrices, Xiangtan University Master's Press (2007).

[2] Zhijie Yuan, The Research on the Computing Problems and the Properties about Special Matrices, Northwestern Polytechnical University Master's Thesis (2005).

[3] Jingliang Chen, Xianghui Chen, Special Matrix, Tsinghua University Press(2001).

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

[5] Xiao Zhonghui, Wang Liping, Zheng Tiesheng, Rapid Algoritlm to Jacobi Matrices of Nonlinear Oil-film Forces in Journal Bearings, Chinese Journal of Applied Mechanics, Vol. 22(2005) , pp.67-70.

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

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

[7] 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

[8] 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

[9] 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

[10] 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.

[11] 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.

[12] 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.

[13] 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.

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

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

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