相关论文: Block bond-order potential as a convergent moments…

Efficient matrix trace estimation is essential for scalable computation of log-determinants, matrix norms, and distributional divergences. In many large-scale applications, the matrices involved are too large to store or access in full,…

We analyze a zeroth-order particle algorithm for the global optimization of a non-convex function, focusing on a variant of Consensus-Based Optimization (CBO) with small but fixed noise intensity. Unlike most previous studies restricted to…

Bond-order potentials (BOPs) provide a local and physically transparent description of the interatomic interaction. Here we describe the efficient implementation of analytic BOPs in the BOPfox program and library. We discuss the integration…

We improve the convergence of the Lanczos algorithm using the matrix product state representation. As an alternative to the density matrix renormalization group (DMRG), the Lanczos algorithm avoids local minima and can directly find…

The increasing imbalance between the computing capabilities of individual nodes and the internode bandwidth makes it highly desirable for any Lattice QCD algorithm to minimize the amount of internode communication. One of the relatively new…

Using a super-operator formulation of linearized time-dependent density-functional theory, the dynamical polarizability of a system of interacting electrons is given a matrix continued-fraction representation whose coefficients can be…

We suggest a method to compute approximations to temporal correlation functions of few-body observables in chaotic many-body systems in the thermodynamic limit based on the respective Lanczos coefficients. Given the knowledge of these…

The recursion method, which solves coupled Heisenberg equations in a Lanczos operator basis, has recently emerged as a powerful nonperturbative tool for computing dynamical correlation functions in strongly correlated two- and…

We establish rigourously the scaling properties of the Lanczos process applied to an arbitrary extensive Many-Body System which is carried to convergence n to infinity and the thermodynamic limit N to infinity taken. In this limit the…

We propose a new concept of a relatively inexact stochastic subgradient and present novel first-order methods that can use such objects to approximately solve convex optimization problems in relative scale. An important example where…

We propose a thick-restart block Lanczos method, which is an extension of the thick-restart Lanczos method with the block algorithm, as an eigensolver of the large-scale shell-model calculations. This method has two advantages over the…

Bond-order potentials (BOPs) are derived from the tight-binding (TB) approximation and provide a linearly-scaling computation of the energy and forces for a system of interacting atoms. While the numerical BOPs involve the numerical…

An iterative algorithm is presented for solving the RPA equations of linear response. The method optimally computes the energy-weighted moments of the strength function, allowing one to match the computational effort to the intrinsic…

The linear combination of atomic orbitals (LCAO) is a standard method for studying solids and molecules, it is also known as the tight$-$binding (TB) method. In most of the implementations only the basis set and the coupling constants are…

Lanczos methods for solving $\textit{A}\textbf{x}=\textbf{b}$ consist in constructing a sequence of vectors $(\textbf{x}_k), k=1,...$ such that $\textbf{r}_{k}=\textbf{b}-\textit{A}\textbf{x}_{k}=\textit{P}_{k}(\textit{A})\textbf{r}_{0}$,,…

It is shown that, an entire class of off-diagonally disordered linear lattices composed of two basic building blocks and described within a tight binding model can be tailored to generate absolutely continuous energy bands. It can be…

Energy-dependent sum rules are useful tools in many fields of physics. In nuclear physics, they typically involve an integration of the response function over the nuclear spectrum with a weight function composed of integer powers of the…

Our goal in this paper is to clarify the relationship between the block Lanczos and the block conjugate gradient (BCG) algorithms. Under the full rank assumption for the block vectors, we show the one-to-one correspondence between the…

In this paper, we revisit the generalized block power methods for approximating the eigenvector associated with $\lambda_1 = 1$ of a Markov chain transition matrix. Our analysis of the block power method shows that when $s$ linearly…

Computing the null space of a large sparse matrix $A$ is a challenging computational problem, especially if the nullity -- the dimension of the null space -- is not small. When applying a block Lanczos method to $A^\mathsf{T} A$ for this…