The computation of the eigenvalue decomposition of matrices is
one of the most investigated problems in numerical linear algebra. In particular,
real nonsymmetric tridiagonal eigenvalue problems arise in a variety of
applications. In this paper the problem of computing an eigenvector corresponding
to a known eigenvalue of a real nonsymmetric tridiagonal matrix is
considered, developing an algorithm that combines part of a QR sweep and
part of a QL sweep, both with the shift equal to the known eigenvalue. The
numerical tests show the reliability of the proposed method.