Related papers: LREI: A fast numerical solver for quantum Landau-L…
We consider high order, implicit Runge-Kutta schemes to solve time-dependent stiff PDEs on dynamically adapted grids generated by multiresolution analysis for unsteady problems disclosing localized fronts. The multiresolution finite volume…
Lexicographically minimal string rotation (LMSR) is a problem to find the minimal one among all rotations of a string in the lexicographical order, which is widely used in equality checking of graphs, polygons, automata and chemical…
We propose a symmetric low-rank representation (SLRR) method for subspace clustering, which assumes that a data set is approximately drawn from the union of multiple subspaces. The proposed technique can reveal the membership of multiple…
Low-rank and sparse composite approximation is a natural idea to compress Large Language Models (LLMs). However, such an idea faces two primary challenges that adversely affect the performance of existing methods. The first challenge…
Dynamical low-rank approximation allows for solving large-scale matrix differential equations (MDEs) with significantly fewer degrees of freedom and has been applied to a growing number of applications. However, most existing techniques…
Answering the question of existence of efficient quantum algorithms for NP-hard problems require deep theoretical understanding of the properties of the low-energy eigenstates and long-time coherent dynamics in quantum spin glasses. We…
Using the invariant operator method for an effective Hamiltonian including the radiation-spin interaction, we describe the quantum theory for magnetization dynamics when the spin system evolves nonadiabatically and out of equilibrium, $d…
We investigate low-regularity integrator (LRI) methods for the Q-tensor model governing nematic liquid-crystalline semilinear parabolic equation. First- and second-order temporal discretizations are developed using Duhamel's formula, and we…
In this paper, we propose a low rank approximation method for efficiently solving stochastic partial differential equations. Specifically, our method utilizes a novel low rank approximation of the stiffness matrices, which can significantly…
We generalize the concept of the Wehrl entropy of quantum states which gives a basis-independent measure of their localization in phase space. We discuss the minimal values and the typical values of these R{enyi-Wehrl entropies for pure…
Low-rank approximation is a technique to approximate a tensor or a matrix with a reduced rank to reduce the memory required and computational cost for simulation. Its broad applications include dimension reduction, signal processing,…
Solving linear systems is at the foundation of many algorithms. Recently, quantum linear system algorithms (QLSAs) have attracted great attention since they converge to a solution exponentially faster than classical algorithms in terms of…
We propose a model order reduction framework for incompressible fluid-structure interaction (FSI) problems based on high-order implicit Runge-Kutta (IRK) methods. We consider separate reduced spaces for fluid velocity, fluid pressure and…
In this paper we provide some uniqueness results for the (multi-)coefficient identification problem of reconstructing the spatially varying spin density as well as the spin-lattice and spin-spin relaxation times and the local field…
Matrix equations are omnipresent in (numerical) linear algebra and systems theory. Especially in model order reduction (MOR) they play a key role in many balancing based reduction methods for linear dynamical systems. When these systems…
We propose a rank-one Riemannian subspace descent algorithm for computing symmetric positive definite (SPD) solutions to nonlinear matrix equations arising in control theory, dynamic programming, and stochastic filtering. For solution…
The method of quantum tomography, which allows us to track with high accuracy the evolution of multilevel quantum systems (qudits) in Hilbert spaces of various dimensions is presented. The developed algorithms for quantum control are based…
Large Language Models (LLMs) have enabled remarkable progress in natural language processing, yet their high computational and memory demands pose challenges for deployment in resource-constrained environments. Although recent low-rank…
Projected gradient descent and its Riemannian variant belong to a typical class of methods for low-rank matrix estimation. This paper proposes a new Nesterov's Accelerated Riemannian Gradient algorithm by efficient orthographic retraction…
Solving complex partial differential equations is vital in the physical sciences, but often requires computationally expensive numerical methods. Reduced-order models (ROMs) address this by exploiting dimensionality reduction to create fast…