We develop a technique for generating a set of optimized local basis functions to solve models in the Kohn–Sham density functional theory for both insulating and metallic systems. The optimized local basis functions are obtained by solving a minimization problem in an admissible set determined by a large number of primitive basis functions. Using the optimized local basis set, the electron ener...

Newton iteration is a standard tool for the numerical solution of nonlinear partial diierential equations. We show how globally supported multiquadric radial basis functions can be used for this task. Some experiments with Nash iteration are also included.

Several representations for the interpolating polynomial exist: Lagrange, Newton, orthogonal polynomials etc. Each representation is characterized by some basis functions. In this paper we investigate the transformations between the basis functions which map a specific representation to another. We show that for this purpose the LU and the QR decomposition of the Vandermonde matrix play a cruci...

Two mismatch functions (power or current) and three coordinates (polar, Cartesian and complex form) result in six versions of the Newton–Raphson method for the solution of power flow problems. In this paper, five new versions of the Newton power flow method developed for single-phase problems in our previous paper are extended to three-phase power flow problems. Mathematical models of the load,...

Two mismatch functions (power or current) and three coordinates (polar, Cartesian and complex form) result in six versions of the Newton–Raphson method for the solution of power flow problems. In this paper, five new versions of the Newton power flow method developed for single-phase problems in our previous paper are extended to three-phase power flow problems. Mathematical models of the load,...

Resistant training in radial basis function (RBF) networks is the topic of this paper. In this paper, one modification of Gauss-Newton training algorithm based on the theory of robust regression for dealing with outliers in the framework of function approximation, system identification and control is proposed. This modification combines the numerical robustness of a particular class of non-quad...

Various problems lead to the same class of functions from integers to integers: functions having integral difference ratio, i.e. verifying f(a) − f(b) ≡ 0 (mod (a − b)) for all a > b. In this paper we characterize this class of functions from Z to Z via their à la Newton series expansions on a suitably chosen basis of polynomials (with rational coefficients). We also exhibit an example of such ...