• Topics:
• Numerical Linear Algebra

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Citation

• 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:
  
  @article{dhillon1998reliablec, author = "Inderjit S. Dhillon", title = "Reliable computation of the Condition Number of a Tridiagonal Matrix in O(n) Time", journal = "SIAM Journal of Matrix Analysis and Applications (SIMAX)", page = "776–796", volume = "19", issue = "3", year = "1998", month = "jul", abstract = "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." }