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A practical high-accuracy relativistic method of atomic structurecalculations for univalent atoms is presented. The method is rooted in thecoupled-cluster formalism and includes non-perturbative treatment of single anddouble excitations from the core and single, double and triple excitationsinvolving valence electron. Triple excitations of core electrons are includedin the fourth-order of many-body perturbation theory. In addition,contributions from the disconnected excitations are incorporated. Evaluation ofmatrix elements includes all-order dressing of lines and vertices of thediagrams. The resulting formalism for matrix elements is complete through thefourth order and sums certain chains of diagrams to all orders. With thedeveloped method we compute removal energies, magnetic-dipolehyperfine-structure constants A and electric-dipole amplitudes. We find thatthe removal energies are reproduced within 0.01-0.03% and the hyperfineconstants of the 3s_1/2 and 3p_1/2 states with a better than 0.1% accuracy. Thecomputed dipole amplitudes for the principal 3s_1/2 - 3p_1/2;3/2 transitionsare in an agreement with 0.05%-accurate experimental data.Comment: 14 pages, 5 figures (accepted for publication in Physical Review A

Triple excitations in the relativistic coupled-cluster formalism and calculation of Na properties