Tensor Approximation of Slater-Type Orbital Basis Functions

Linear augmented Slater-type orbital method for free standing clusters

We have developed a Scalable Linear Augmented Slater-Type Orbital (LASTO) method for electronic-structure calculations on free-standing atomic clusters. As with other linear methods we solve the Schrödinger equation using a mixed basis set consisting of numerical functions inside atom-centered spheres and matched onto tail functions outside. The tail functions are Slater-type orbitals, which ar...

Nonlinear tensor product approximation of functions

We are interested in approximation of a multivariate function f(x1, . . . , xd) by linear combinations of products u (x1) · · ·u(xd) of univariate functions u(xi), i = 1, . . . , d. In the case d = 2 it is the classical problem of bilinear approximation. In the case of approximation in the L2 space the bilinear approximation problem is closely related to the problem of singular value decomposit...

Approximation of a Fuzzy Function by Using Radial Basis Functions Interpolation

In the present paper, Radial Basis Function interpolations are applied to approximate a fuzzy function $tilde{f}:Rrightarrow mathcal{F}(R)$, on a discrete point set $X={x_1,x_2,ldots,x_n}$, by a fuzzy-valued function $tilde{S}$. RBFs are based on linear combinations of terms which include a single univariate function. Applying RBF to approximate a fuzzy function, a linear system wil...

Basis set construction for molecular electronic structure theory: natural orbital and Gauss-Slater basis for smooth pseudopotentials.

A simple yet general method for constructing basis sets for molecular electronic structure calculations is presented. These basis sets consist of atomic natural orbitals from a multiconfigurational self-consistent field calculation supplemented with primitive functions, chosen such that the asymptotics are appropriate for the potential of the system. Primitives are optimized for the homonuclear...

Numerical Solution of Singular IVPs of Lane-Emden Type Using Integral Operator and Radial Basis Functions