Related papers: Thick-Restart Block Lanczos Method for Large-Scale…
Simulating complex spin systems, known for high frustration and entanglement, presents significant challenges due to their intricate energy landscapes. This study focuses on the $J_{1}-J_{2}$ Heisenberg model, renowned for its rich phase…
To understand the dynamics of quantum many-body systems, it is essential to study excited eigenstates. While tensor network states have become a standard tool for computing ground states in computational many-body physics, obtaining…
The Levenberg-Marquardt (LM) method is commonly used for inverting models used to describe geothermal, groundwater, or oil and gas reservoirs. In previous studies LM parameter updates have been made tractable for highly parameterized…
This work introduces a method for determining the energy spectrum of lattice quantum chromodynamics (LQCD) by applying the Lanczos algorithm to the transfer matrix and using a bootstrap generalization of the Cullum-Willoughby method to…
We present an ab initio approach for the description of collective excitations and transition strength distributions of arbitrary nuclei up into the sd-shell that based on the No-Core Shell Model in combination with the Lanczos…
We introduce a numerical method for computing spectral densities, and apply it to the evaluation of the local density of states (LDOS) of sparse Hamiltonians derived from tight-binding models. The approach, which we call the high-order…
Study of the N ~ Z nuclei in the mass-80 region is not only interesting due to the existence of abundant nuclear structure phenomena, but also important in understanding the nucleosynthesis in the rp-process. It is not feasible to apply a…
The density-matrix renormalization group (DMRG) algorithm can be adapted to the calculation of dynamical correlation functions in various ways which all represent compromises between computational efficiency and physical accuracy. In this…
The present review will focus on recent development of exact-diagonali- zation (ED) methods that use Lanczos algorithm to transform large sparse matrices onto the tridiagonal form. We begin with a review of basic principles of the Lanczos…
Various methods have been developed for the quantum computation of the ground and excited states of physical and chemical systems, but many of them require either large numbers of ancilla qubits or high-dimensional optimization. The quantum…
We develop a distributed Block Chebyshev-Davidson algorithm to solve large-scale leading eigenvalue problems for spectral analysis in spectral clustering. First, the efficiency of the Chebyshev-Davidson algorithm relies on the prior…
We devise and evaluate numerically Hybrid High-Order (HHO) methods for hyperelastic materials undergoing finite deformations. The HHO methods use as discrete unknowns piecewise polynomials of order $k\ge1$ on the mesh skeleton, together…
We consider the problem of extracting a few desired eigenpairs of the buckling eigenvalue problem $Kx = \lambda K_Gx$, where $K$ is symmetric positive semi-definite, $K_G$ is symmetric indefinite, and the pencil $K - \lambda K_G$ is…
A majority of numerical scientific computation relies heavily on handling and manipulating matrices, such as solving linear equations, finding eigenvalues and eigenvectors, and so on. Many quantum algorithms have been developed to advance…
The Continuum Shell Model is an old but recently revived method that traverses the boundary between nuclear many-body structure and nuclear reactions. The method is based on the non-Hermitian energy-dependent effective Hamiltonian. The…
The spectral decomposition of a real skew-symmetric matrix $A$ can be mathematically transformed into a specific structured singular value decomposition (SVD) of $A$. Based on such equivalence, a skew-symmetric Lanczos bidiagonalization…
We merge two successful ab initio nuclear-structure methods, the no-core shell model (NCSM) and the multi-reference in-medium similarity renormalization group (IM-SRG) to define a new many-body approach for the comprehensive description of…
Recent developments in self-supervised learning give us the possibility to further reduce human intervention in multi-step pipelines where the focus evolves around particular objects of interest. In the present paper, the focus lays in the…
The shell model Monte Carlo (SMMC) approach provides a powerful method for the microscopic calculation of statistical and collective nuclear properties in model spaces that are many orders of magnitude larger than those that can be treated…
The Lanczos algorithm, introduced by Cornelius Lanczos, has been known for a long time and is widely used in computational physics. While often employed to approximate extreme eigenvalues and eigenvectores of an operator, recently interest…