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The development of the relativistic all-order method where all single,double, and partial triple excitations of the Dirac-Hartree-Fock wave functionare included to all orders of perturbation theory led to many important resultsfor study of fundamental symmetries, development of atomic clocks, ultracoldatom physics, and others, as well as provided recommended values of many atomicproperties critically evaluated for their accuracy for large number ofmonovalent systems. This approach requires iterative solutions of thelinearized coupled-cluster equations leading to convergence issues in somecases where correlation corrections are particularly large or lead to anoscillating pattern. Moreover, these issues also lead to similar problems inthe CI+all-order method for many-particle systems. In this work, we haveresolved most of the known convergence problems by applying two differentconvergence stabilizer methods, reduced linear equation (RLE) and directinversion of iterative subspace (DIIS). Examples are presented for B, Al,Zn$^+$, and Yb$^+$. Solving these convergence problems greatly expands thenumber of atomic species that can be treated with the all-order methods and isanticipated to facilitate many interesting future applications.

Resolving all-order method convergence problems for atomic physics applications