Related papers: Thick-Restart Block Lanczos Method for Large-Scale…
The feasibility of shell-model calculations is radically extended by the Quantum Monte Carlo Diagonalization method with various essential improvements. The major improvements are made in the sampling for the generation of shell-model basis…
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…
We introduce a new implementation of time-dependent density-functional theory which allows the \emph{entire} spectrum of a molecule or extended system to be computed with a numerical effort comparable to that of a \emph{single} standard…
The nuclear shell model is one of the prime many-body methods to study the structure of atomic nuclei, but it is hampered by an exponential scaling on the basis size as the number of particles increases. We present a shell-model quantum…
A theory is presented for a novel recursion method for O(N) ab initio tight-binding calculations. A long-standing problem of generalizing the recursion method to a non-orthogonal basis, which is a crucial step to make the recursion method…
Models of quantum systems scale exponentially with the addition of single-particle states, which can present computationally intractable problems. Alternatively, quantum computers can store a many-body basis of $2^n$ dimensions on $n$…
The shell model Monte Carlo (SMMC) method enables calculations in model spaces that are many orders of magnitude larger than those that can be treated by conventional methods, and is particularly suitable for the calculation of level…
The distribution of the eigenvalues of a Hermitian matrix (or of a Hermitian matrix pencil) reveals important features of the underlying problem, whether a Hamiltonian system in physics, or a social network in behavioral sciences. However,…
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,…
In this paper, we present a new approach for model reduction of large scale first and second order dynamical systems with multiple inputs and multiple outputs (MIMO). This approach is based on the projection of the initial problem onto…
The GW approximation is widely used for reliable and accurate modeling of single-particle excitations. It also serves as a starting point for many theoretical methods, such as its use in the Bethe-Salpeter equation (BSE) and dynamical…
The shell model Monte Carlo (SMMC) approach allows for the microscopic calculation of statistical and collective properties of heavy nuclei using the framework of the configuration-interaction shell model in very large model spaces. We…
With the emergence of Artificial Intelligence, numerical algorithms are moving towards more approximate approaches. For methods such as PCA or diffusion maps, it is necessary to compute eigenvalues of a large matrix, which may also be dense…
The configuration-interaction shell model approach provides an attractive framework for the calculation of nuclear level densities in the presence of correlations, but the large dimensionality of the model space has hindered its application…
We use quantum Monte Carlo methods in the framework of the interacting nuclear shell model to calculate the statistical properties of nuclei at finite temperature and/or excitation energies. With this approach we can carry out realistic…
We present a newly enhanced version of the Monte Carlo Shell Model method by incorporating the conjugate gradient method and energy-variance extrapolation. This new method enables us to perform large-scale shell-model calculations that the…
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…
The extension of least-squares tensor hypercontracted second- and third-order M{\o}ller-Plessett perturbation theory (LS-THC-MP2 and LS-THC-MP3) to open-shell systems is an important development due to the scaling reduction afforded by THC…
This paper proposes a harmonic Lanczos bidiagonalization method for computing some interior singular triplets of large matrices. It is shown that the approximate singular triplets are convergent if a certain Rayleigh quotient matrix is…
A new iterative method for solving large scale symmetric nonlinear eigenvalue problems is presented. We firstly derive an infinite dimensional symmetric linearization of the nonlinear eigenvalue problem, then we apply the indefinite Lanczos…