- 27.
- If
**FACT**= 'N', a diagonal pivoting method is used to factor the matrix as

or

where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and D is symmetric (**LA_SYSVX**) or Hermitian (**LA_HESVX**) and block diagonal with and diagonal blocks. - 28.
- If some , so that is singular, then the routine returns with . Otherwise, the factored form of is used to estimate the condition number of the matrix . 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.
- 29.
**LA_SYSVX**and**LA_HESVX**also optionally compute, for each solution vector , the estimated forward error bound and the componentwise relative backward error.