Abstract
An accurate, efficient and robust numerical method for the solution of the optimized random phase approximation (ORPA) of classical liquids is presented. The uniqueness of the solution of the ORPA is proved rigorously. The method, hinging on the characterization of the generating functional, improves significantly on previous algorithms. Higher accuracy is obtained by using the values of the unknown functions on the grid points as independent variables instead of the usual coefficients of an expansion in orthogonal polynomials. It is shown that minimizing a suitably modified functional with a conjugate-gradient algorithm results in a very efficient and robust algorithm.
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