Related papers: Automatic Generation of Accurate and Cost-efficien…
An important issue with oversampled FIR analysis filter banks (FBs) is to determine inverse synthesis FBs, when they exist. Given any complex oversampled FIR analysis FB, we first provide an algorithm to determine whether there exists an…
Computing a basis for the exponent lattice of algebraic numbers is a basic problem in the field of computational number theory with applications to many other areas. The main cost of a well-known algorithm…
Randomized sampling has recently been proven a highly efficient technique for computing approximate factorizations of matrices that have low numerical rank. This paper describes an extension of such techniques to a wider class of matrices…
We present an efficient algorithm for one- and two-component relativistic exact-decoupling calculations. Spin-orbit coupling is thus taken into account for the evaluation of relativistically transformed (one-electron) Hamiltonian. As the…
A new method for implementing the kinetic energy operator for real-space, grid-based electronic structure codes is developed. It is based on multi-order Adaptive Finite Differencing (AFD) and uses atomic pseudo orbitals produced by the…
We present an efficient, linear-scaling implementation for building the (screened) Hartree-Fock exchange (HFX) matrix for periodic systems within the framework of numerical atomic orbital (NAO) basis functions. Our implementation is based…
We describe a method of solving the nuclear Skyrme-Hartree-Fock problem by using a deformed Cartesian harmonic oscillator basis. The complete list of expressions required to calculate local densities, total energy, and self-consistent…
Binary optimization, a representative subclass of discrete optimization, plays an important role in mathematical optimization and has various applications in computer vision and machine learning. Usually, binary optimization problems are…
Approximate Bayesian Computation (ABC) has become one of the major tools of likelihood-free statistical inference in complex mathematical models. Simultaneously, stochastic differential equations (SDEs) have developed to an established tool…
The performance of basis sets made of numerical atomic orbitals is explored in density-functional calculations of solids and molecules. With the aim of optimizing basis quality while maintaining strict localization of the orbitals, as…
The evaluation of exact (Hartree--Fock, HF) exchange operator is a crucial ingredient for the accurate description of electronic structure in periodic systems through ab initio and hybrid density functional approaches. An efficient…
We present here an efficient method which systematically reduces the rank of the augmented space and thereby helps to implement augmented space recursion for any real calculation. Our method is based on the symmetry of the Hamiltonian in…
A Radial Basis Function Generated Finite-Differences (RBF-FD) inspired technique for evaluating definite integrals over bounded volumes that have smooth boundaries in three dimensions is described. A key aspect of this approach is that it…
In this paper we obtain approximated numerical solutions for the 2D Helmholtz equation using a radial basis function-generated finite difference scheme (RBF-FD), where weights are calculated by applying an oscillatory radial basis function…
Recent years have seen rapid progress in calculations of gravitational waveforms from asymmetric compact binaries containing spinning secondaries. Here we outline a complete waveform-generation scheme, through first post-adiabatic order…
We develop two variance-reduced fast operator splitting methods to approximate solutions of a class of generalized equations, covering fundamental problems such as \rvs{minimization}, minimax problems, and variational inequalities as…
We present a computationally efficient approach to solve the time-dependent Kohn-Sham equations in real-time using higher-order finite-element spatial discretization, applicable to both pseudopotential and all-electron calculations. To this…
We consider two-dimensional (2D) "artificial atoms" confined by an axially symmetric potential $V(\rho)$. Such configurations arise in circular quantum dots and other systems effectively restricted to a 2D layer. Using the semiclassical…
A new (algebraic) approximation scheme to find {\sl global} solutions of two point boundary value problems of ordinary differential equations (ODE's) is presented. The method is applicable for both linear and nonlinear (coupled) ODE's whose…
Bayesian optimization is a powerful global optimization technique for expensive black-box functions. One of its shortcomings is that it requires auxiliary optimization of an acquisition function at each iteration. This auxiliary…