**We present one more algorithm to compute the condition number (for inversion) of an n × n tridiagonal matrix J in O(n) time. Previous O(n) algorithms for this task given by Higham [SIAM J. Sci. Statist. Comput., 7 (1986), pp. 150–165] are based on the tempting compact representation of the upper (lower) triangle of J^−1 as the upper (lower) triangle of a rank-one matrix. However they suffer from severe overflow and underflow problems, especially on diagonally dominant matrices. Our new algorithm avoids these problems and is as efficient as the earlier algorithms.**

*Abstract:**Topics:*- Numerical Linear Algebra

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- Reliable computation of the Condition Number of a Tridiagonal Matrix in O(n) Time (pdf, software)

I. Dhillon.*SIAM Journal of Matrix Analysis and Applications (SIMAX)*19(3), pp. 776-796, July 1998.*Bibtex:*