相关论文: Multiple Extremal Eigenpairs by the Power Method

This work is concerned with various aspects of the formulation of the quantum inverse scattering method for the one-dimensional Hubbard model. We first establish the essential tools to solve the eigenvalue problem for the transfer matrix of…

We explore the precision with which the Einstein Telescope (ET) will be able to measure the parameters of intermediate-mass-ratio inspirals (IMRIs). We calculate the parameter estimation errors using the Fisher Matrix formalism and present…

Maximum-likelihood exponent maps have been studied as a technique to increase the understanding and improve the fit of power-law exponents to experimental and numerical simulation data, especially when they exhibit both upper and lower…

We have investigated the exceptional points (EPs) which are degeneracies of a non-Hermitian Hamiltonian, in the case that three modes are interacting with each other. Even though the parametric evolution of the modes cannot be uniquely…

We describe algorithms for computing eigenpairs (eigenvalue-eigenvector pairs) of a complex $n\times n$ matrix $A$. These algorithms are numerically stable, strongly accurate, and theoretically efficient (i.e., polynomial-time). We do not…

Matching on covariates is a well-established framework for estimating causal effects in observational studies. The principal challenge stems from the often high-dimensional structure of the problem. Many methods have been introduced to…

We develop a highly efficient framework for computing the thermal entropy in the doped Fermi-Hubbard model within the grand-canonical ensemble. The framework comprises four calculation schemes that express the entropy as path integrals in…

A general method to derive the master equations for extremal models is established. These systems are shown to develop a peculiar kind of correlations between elements related to the characterization of extremal dynamics as an information…

'Causal' direction is of great importance when dealing with complex systems. Often big volumes of data in the form of time series are available and it is important to develop methods that can inform about possible causal connections between…

We represent low dimensional quantum mechanical Hamiltonians by moderately sized finite matrices that reproduce the lowest O(10) boundstate energies and wave functions to machine precision. The method extends also to Hamiltonians that are…

This paper is about computationally tractable methods for power system parameter estimation and Optimal Experiment Design (OED). Here, the main motivation is that OED has the potential to significantly increase the accuracy of power system…

In this paper, we investigate exceptional sets in the Waring-Goldbach problem for unlike powers. For example, estimates are obtained for sufficiently large integers below a parameter subject to the necessary local conditions that do not…

The aim of this paper is to prove an improved version of the bounded differences inequality for matrix valued functions, by developing the methods of Mackey et al.: "Matrix Concentration Inequalities via the Method of Exchangeable Pairs".…

The parallel orbital-updating approach is an orbital/eigenfunction iteration based approach for solving eigenvalue problems when many eigenpairs are required. It has been proven to be efficient, for instance, in electronic structure…

The history of research on eigenvalue problems is rich with many outstanding contributions. Nonetheless, the rapidly increasing size of data sets requires new algorithms for old problems in the context of extremely large matrix dimensions.…

Numerical methods for the transmission eigenvalue problems are hot topics in recent years. Based on the work of Lin and Xie [Math. Comp., 84(2015), pp. 71-88], we build a multigrid method to solve the problems. With our method, we only need…

Traditional dynamic security assessment faces challenges as power systems are experiencing a transformation to inverter-based-resource (IBR) dominated systems, for which electromagnetic transient (EMT) dynamics have to be considered.…

A strictly truncated (weak-coupling) perturbation theory is applied to the attractive Holstein and Hubbard models in infinite dimensions. These results are qualified by comparison with essentially exact Monte Carlo results. The second order…

Impedance models of power systems are useful when state-space models of apparatus such as inverter-based resources (IBRs) have not been made available and instead only black-box impedance models are available. For tracing the root causes of…

We revisit the relative perturbation theory for invariant subspaces of positive definite matrix pairs. As a prototype model problem for our results we consider parameter dependent families of eigenvalue problems. We show that new estimates…