RAN Rui-sheng, HUANG Ting-zhu, LIU Xing-ping, GU Tong-xiang. Algorithm for the Inverse of a General Tridiagonai Matrix[J]. Applied Mathematics and Mechanics, 2009, 30(2): 238-244.
 Citation: RAN Rui-sheng, HUANG Ting-zhu, LIU Xing-ping, GU Tong-xiang. Algorithm for the Inverse of a General Tridiagonai Matrix[J]. Applied Mathematics and Mechanics, 2009, 30(2): 238-244.

# Algorithm for the Inverse of a General Tridiagonai Matrix

• Rev Recd Date: 2008-11-27
• Publish Date: 2009-02-15
• An algorithm for the inverse of a general tridiagonal matrix is presented. First, for the tridiagonal matzix having Doolittle factorization, an algorithm for the inverse was established. Then the algorithm was generalized to a general tridiagonal matrix without aqy restrictive condition. Some comparison with other methods operations of the algorithm for the inverse was discussed in the end. It is shown that the arithmetic operations of the algorithm are low and it is applicable to a general tridiagonal matrix.
•  [1] El-Mikkawy M E A. On the inverse of a general tridiagonal matrix[J].Applied Mathematics and Computation,2004,150(3):669-679. [2] Ranjan K M. The inverse of a tridiagonal matrix[J].Linear Algebra and Its Applications,2001,325(1/3):109-139. [3] Meurant G. A review on the inverse of symmetric tridiagonal and block tridiagonal matrices[J].SIAM Journal on Matrix Analysis and Applications,1992,13(3):707-728. doi: 10.1137/0613045 [4] Nabben R. Decay rates of the inverse of nonsymmetric tridiagonal and band matrix[J]. SIAM Journal on Matrix Analysis and Applications,1999,20(3):820-837. [5] El-Mikkawy M E A. An algorithm for solving tridiagonal systems[J].Journal of Institute of Mathematics and Computer Sciences,1991，4(2):205-210. [6] 丁丽娟. 数值计算方法[M]. 北京: 北京理工大学出版社, 1997, 113-115.

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