The performance of solving a system of linear equations depends on the condition number of the coefficient matrix. Therefore, condition number or its reciprocal RCOND, is an indicator one can examine before computing the solution. If the the value of RCOND is less than the machine epsilon, it indicates that the system is too ill-conditioned to obtain a meaningful solution.
Scaling can substantially reduce the condition number of a linear system. The procedure of scalling is known as equilibration.
Scaling methods include row scaling, column scaling, and row-column scaling. LAPACK routines apply appropriate techniques for equilibrating matrices depending on the input data.