- 9.
- If = 'N', the decomposition is used to factor the matrix as , where is a product of permutation and unit lower bidiagonal matrices and is upper triangular with nonzeros in only the main diagonal and first two superdiagonals.
- 10.
- If some , so that is singular, then the routine returns with . Otherwise, the factored form of is used to estimate the condition number of . If the reciprocal of the condition number is less than machine precision, , where is the order of , is returned as a warning. However, the routine still goes on to solve for . Iterative refinement is applied to improve the computed solution.
- 11.
**LA_GTSVX**also optionally computes, for each solution vector the estimated forward error bound and the componentwise backward error.

Susan Blackford 2001-08-19