Extending LINPACK by verification routines for linear systems Original Research Article

LINPACK is a well known and heavily used software library which offers a collection of routines to solve linear algebra problems. A major drawback of LINAPACK and similar packages is the fact that the provided routines merely compute an approximation for the solution of a given problem. In some cases, a user can get an estimation of the achieved accuracy, but these estimations may give way to a misleading interpretation of the computed solution. Therefore, we show how to extend several LINPACK procedures by the capability of computing a guaranteed inclusion of the solution. For solving linear systems based on factorizations (e.g. LU or Cholesky method), this extension can be established without changing the given library, thus reusing the existing software. Furthermore, runtime and accuracy measurements show for H-matrices that the verification can be achieved with less costs than the computation of the estimation—especially for banded matrices of high dimension.