Abstract—This paper makes an investigation on solving a kind of almost tridiagonal linear equations. By means of exploring more general a system of the Top-Bottom-Bordered Tridiagonal (TBBT) linear equations, the paper obtains an algorithm that costs less than the LU decomposition approach to solve the almost tridiagonal linear equations. Detail mathematical reasoning is presented to derive and analyze the algorithm. Numerical experiments show the algorithm can be applied to engineering application within expectation.

Key words—Tridiagonal linear equations; Woodbury matrix identity, matrix Inverse, engineering computation

Xingbo Wang is with Department of Mechatronics, Foshan University, Guangdong, China and Guangdong College of Applied Science and Technology, Guangdong, China. Jue Wang is with Shenzhen Smoore Technology Co., Ltd., Guangdong, China.

Cite:Xingbo Wang, Jue Wang, "On the Solution of an Almost Tridiagonal Linear Equations," International Journal of Applied Physics and Mathematics vol. 13, no. 3, pp. 34-43, 2023.

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