Volume 34 • Number 2 • 2011   • Inverses of Block Tridiagonal Matrices and Rounding Errors Chi-Ye Wu, Ting-Zhu Huang, Liang Li and Xiao-Guang Lv Abstract. Based on URV-decomposition in Stewart [An updating algorithm for subspace tracking, IEEE Trans. Signal Processing, 40 (1992): 1535--1541] and the result of Mehrmann [Divide and conquer methods for block tridiagonal systems, \emph{Parallel Comput.}, 19 (1993): 257--279], inverses of block tridiagonal matrices are presented. The computational complexity of the proposed algorithm is less than that of the Block Gaussian-Jordan Elimination method when the orders of the matrices are not less than 100. Expressions for the rounding errors incurred during the process of the computation of the inverses of block tridiagonal matrices are also considered. Moreover, from the experiment, it shows that the norms of the errors generated from the Block Gaussian-Jordan Elimination method are larger than those of the proposed algorithm. 2010 Mathematics Subject Classification: 65F05, 65G50, 65Y20. Full text: PDF