相关论文: Solvers for the Hermitian and the pseudo-Hermitian…
A new integrable model which is a variant of the one-dimensional Hubbard model is proposed. The integrability of the model is verified by presenting the associated quantum R-matrix which satisfies the Yang-Baxter equation. We argue that the…
The paper describes a sparse direct solver for the linear systems that arise from the discretization of an elliptic PDE on a two dimensional domain. The scheme decomposes the domain into thin subdomains, or ``slabs'' and uses a two-level…
The spectral transformation Lanczos method for the sparse symmetric definite generalized eigenvalue problem for matrices $A$ and $B$ is an iterative method that addresses the case of semidefinite or ill conditioned $B$ using a shifted and…
The maximum density still life problem (MDSLP) is a hard constraint optimization problem based on Conway's game of life. It is a prime example of weighted constrained optimization problem that has been recently tackled in the…
We provide exact analytical solutions for a two dimensional explicitly time-dependent non-Hermitian quantum system. While the time-independent variant of the model studied is in the broken PT-symmetric phase for the entire range of the…
Simulating quantum dynamics on classical computers is challenging for large systems due to the significant memory requirements. Simulation on quantum computers is a promising alternative, but fully optimizing quantum circuits to minimize…
Simulations of isolated binary mergers of galaxy clusters are a useful tool to study the evolution of these objects. For exceptionally massive systems they even represent the only viable way of simulation, because these are rare in typical…
We first consider the problem of approximating a few eigenvalues of a rational matrix-valued function closest to a prescribed target. It is assumed that the proper rational part of the rational matrix-valued function is expressed in the…
Many complex systems can be reduced to their key components through spectrally decomposing matrices that capture their dynamics. These matrices can in turn be constructed from data, often by least-squares fitting: examples of algorithms to…
We review existing methods for implementing smooth functions f(A) of a sparse Hermitian matrix A on a quantum computer, and analyse a further combination of these techniques which has some advantages of simplicity and resource consumption…
We treat infinite horizon optimal control problems by solving the associated stationary Hamilton-Jacobi-Bellman (HJB) equation numerically to compute the value function and an optimal feedback law. The dynamical systems under consideration…
We consider the solution of nonlinear programs with nonlinear semidefiniteness constraints. The need for an efficient exploitation of the cone of positive semidefinite matrices makes the solution of such nonlinear semidefinite programs more…
The Gaudin model based on the sl_2-invariant r-matrix with an extra Jordanian term depending on the spectral parameters is considered. The appropriate creation operators defining the Bethe states of the system are constructed through a…
In this paper, Sphere Decoding (SD) algorithms for Spatial Modulation (SM) are developed to reduce the computational complexity of Maximum-Likelihood (ML) detectors. Two SDs specifically designed for SM are proposed and analysed in terms of…
Backward error (BE) analysis emerges as a powerful tool for assessing the backward stability and strong backward stability of numerical algorithms. In this paper, we explore structured BEs for a class of double saddle point problems…
We present an algorithm and its parallel implementation for solving a self consistent problem as encountered in Hartree Fock or Density Functional Theory. The algorithm takes advantage of the sparsity of matrices through the use of local…
This paper presents an efficient framework for private Transformer inference that combines Homomorphic Encryption (HE) and Secure Multi-party Computation (MPC) to protect data privacy. Existing methods often leverage HE for linear layers…
In this paper, we propose iterative inner/outer approximations based on a recent notion of block factor-width-two matrices for solving semidefinite programs (SDPs). Our inner/outer approximating algorithms generate a sequence of upper/lower…
When applying eigenvalue decomposition on the quadratic term matrix in a type of linear equally constrained quadratic programming (EQP), there exists a linear mapping to project optimal solutions between the new EQP formulation where $Q$ is…
The numerical analysis for the small amplitude motion of an elastic beam with internal damping is investigated in domain with moving ends. An efficient numerical method is constructed to solve this moving boundary problem. The stability and…