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For an $n \times n$ tridiagonal matrix we exploit the structure of   its  QR factorization to devise two new algorithms for computing the 1-norm   condition number in $O(n)$ operations.  The algorithms avoid   underflow and overflow, and are simpler than existing algorithms since   tests are not required for degenerate cases.  An error analysis of the   first algorithm is given, while the second algorithm is shown to be   competitive in speed with existing algorithms.  We then turn our   attention to an $n \times n$ diagonal-plus-semiseparable matrix, $A$,   for which several algorithms have recently been developed to solve   $Ax=b$ in $O(n)$ operations.  We again exploit the QR factorization of   the matrix to present an algorithm that computes the 1-norm condition   number in $O(n)$ operations

Computing the Condition Number of Tridiagonal and Diagonal-Plus-Semiseparable Matrices in Linear Time