An Efficient Gauss-Newton-like Method for the Numerical Solution of the Ornstein-Zernike Integral Equation for a Class of Fluid Models

Solvation Thermodynamics of Organic Molecules by the Molecular Integral Equation Theory: Approaching Chemical Accuracy

“…We note that the Newton-Raphson (NR) method itself is not typically an efficient way to solve IET equations because it requires the calculation and inversion of a large Jacobian matrix. In this hybrid methods, the dimensionality of the Newton-Raphson part is reduced by expansions of the IET equations in basis sets of roof functions, 244 plane waves [245][246][247] or wavelets. 221,248,249 In the third category are procedures for solving the OZ equation using matrix-free iterative Krylov or Newton-GMRES solvers.…”

In Silico Screening of Bioactive and Biomimetic Solutes Using Molecular Integral Equation Theory

“…In the first category there are methods based on Picard iterations with techniques like vector extrapolation or iterative subspace extrapolation used to improve the convergence [42,[48][49][50]. In the second category there are hybrid Newton-Raphson/Picard iteration methods [51][52][53][54][55][56][57][58][59][60], which have been combined with expansions of the RISM equations in basis sets of roof functions [51], plane waves [52,55,60] or wavelets [57][58][59]. We note that the Newton-Raphson (NR) method cannot typically be applied directly to solve the RISM equations because it would require the calculation and inversion of a Jacobian matrix of a size > 10 4 .…”