Fast Algorithm for the Inverse Matrices of Periodic Adding Element Tridiagonal Matrices

Abstract:

Adding element tridiagonal periodic matrices have an important effect for the algorithms of solving linear systems，computing the inverses, the triangular factorization，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.

• Periodical: Advanced Materials Research (Volume 159)
• Pages: 464-468
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.159.464
• Online since: December 2010
• Authors: Hong Ling Fan
• Keywords: Inverse Matrix, Periodic Adding Element Tridiagonal Matrices, Periodic Tridiagonal Matrices, Tridiagonal Matrices

References

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

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

[3] 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) , p.67–72.

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

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

[5] YUAN Zhi-jie, The Research on the Computing Problems and the ProPerties about Special Matrices, Northwestern Polytechnical University Master's Press (2005).

[6] 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

[7] 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

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

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

[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 (Natural Science, 23 (2003) 5-7.

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

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

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

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

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

[22] 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

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

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