Error bounds on the solution and a condition estimate are also provided.
U is upper triangular with nonzeros in only the main diagonal and first two superdiagonals. If the reciprocal of the condition number is less than machine precision, steps 3 and 4 are skipped. The system of equations is solved for X using the factored form of A. 4. Iterative refinement is applied to improve the computed solution matrix and calculate error bounds and backward error estimates for it.