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

Abstract:

The theory and method of matrix computation, as an important tool, have much important applications such as in computational mathematics, physics, image processing and recognition, missile system design, rotor bearing system, nonlinear kinetics, economics and biology etc. 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 period matrices.

• Periodical: Advanced Materials Research (Volume 159)
• Pages: 459-463
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.159.459
• Online since: December 2010
• Authors: Hong Ling Fan
• Keywords: Inverse Matrix, Lower Bound, Signal Processing, Strictly Diagonally Dominant, Tridiagonal Matrices

References

[1] Zhang Houzhu, Zhang Yu, Sun Zheng, Implicit splitting finite difference Scheme for numerical simulation of multi-dimensional Wave equation, Geophysical Prospecting for Petroleum, Vol. 46(2007) , p.594–597.

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

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

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

DOI: 10.1016/j.aml.2005.08.009

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

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

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

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

[9] 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.

[10] 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.

[11] 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.

[12] 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.

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

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

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