We developed a program code of configuration interaction singles (CIS) based on a numerical grid method. We used Kohn-Sham (KS) as well as Hartree-Fock (HF) orbitals as a reference configuration and Lagrange-sinc functions as a basis set. Our calculations show that KS-CIS is more cost-effective and more accurate than HF-CIS. The former is due to the fact that the non-local HF exchange potential...

Under suitable conditions on a measure, universality limits f ( ; ) that arise in the bulk, unitary case, are reproducing kernels of de Branges spaces of entire functions. In the classical case, f is the sinc kernel f (s; t) = sin (s t) (s t) ; but other kernels can arise. We study the linear operator L [h] (x) = Z 1 1 f (s; x)h (s) ds; establishing inequalities, and deducing some conditions fo...

We discuss a new approach to represent fractional operators by Sinc approximation using convolution integrals. A spin off of the convolution representation is an effective inverse Laplace transform. Several examples demonstrate the application of the method to different practical problems.

The fully Sinc-Galerkin method is developed for a family of complex-valued partial differential equations with time-dependent boundary conditions. The Sinc-Galerkin discrete system is formulated and represented by a Kronecker product form of those equations. The numerical solution is efficiently calculated and the method exhibits an exponential convergence rate. Several examples, some with a re...

The Sinc quadrature and the Sinc indefinite integration are approximation formulas for definite integration and indefinite integration, respectively, which can be applied on any interval by using an appropriate variable transformation. Their convergence rates have been analyzed for typical cases including finite, semi-infinite, and infinite intervals. In addition, for verified automatic integra...

in this paper, a numerical solution for a system of linear fredholm integro-differential equations by means of the sinc method is considered. this approximation reduces the system of integro-differential equations to an explicit system of algebraic equations. the exponential convergence rate $o(e^{-k sqrt{n}})$ of the method is proved. the analytical results are illustrated with numerical examp...

A fast multilevel algorithm (MuST) for evaluating an n-sample sinc interpolant at mn points is presented. For uniform grids, its complexity is 25mn log(1/δ) flops for the sinc kernel and 75mn log(1/δ) for the sincd kernel, where δ is the target evaluation accuracy. MuST is faster than FFTand FMM-based evaluations for large n and/or for large δ. It is also applicable to non-uniform grids and to ...

Using coherent-state techniques, we prove a sampling theorem for Majorana's (holomor-phic) functions on the Riemann sphere and we provide an exact reconstruction formula as a convolution product of N samples and a given reconstruction kernel (a sinc-type function). We also discuss the effect of over-and under-sampling. Sample points are roots of unity, a fact which allows explicit inversion for...