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The generalized Lloyd formula and the trace of the Green's function are equivalent expressions for the number of states of electrons in solids. The comparison of these two approaches enables one to estimate the accuracy of the number-of-states calculations. We study the accuracy of the Lloyd formula and of the trace of the Green's function for the number of states of a binary random alloy as a function of the cutoff parameter t " in the orbital momentum representation. We show that for transition metals truncation at t "=2 leads to an essential loss of accuracy. It is necessary to take into consideration the contributions of s, p, d, and f electrons in both approaches to obtain their numerical equivalence. All higher-L contributions can be neglected. We propose a quadratic extrapolation scheme to solve the coherent-potential-approximation equation in one iteration. We show that the use of the tetrahedron technique for the Brillouin-zone integration for calculation of the r matrix of an alloy allows us to obtain high-precision results with minimum computational efForts. The proposed procedures reduce computational time at least by a factor of 100 in comparison with the standard approaches.

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It is shown that the Brillouin zone integral for the interstitial KKR Green function can be evaluated accurately by taking proper care of the free-electron singularities in the integrand. The proposed method combines two recently developed methods, a supermatrix method and a subtraction method. This combination appears to provide a major improvement compared with an earlier proposal based on the subtraction method only. Consequently, the barrier preventing the study of important interstitial-like defects, such as an electromigrating atom halfway along its jump path, can be considered as being razed. ͓S0163-1829͑96͒07228-1͔

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