Related papers: A New Highly Parallel Non-Hermitian Eigensolver

Large-scale earthquake sequence simulations using the boundary element method (BEM) incur extreme computational costs through multiplying a dense matrix with a slip rate vector. Hierarchical matrices (H-matrices) have often been used to…

This paper presents new fast algorithms for Hermite interpolation and evaluation over finite fields of characteristic two. The algorithms reduce the Hermite problems to instances of the standard multipoint interpolation and evaluation…

We consider a new class of non-Hermitian random matrices, namely the ones which have the form of sums of freely independent terms involving unitary matrices. To deal with them, we exploit the recently developed quaternion technique. After…

Most cloud services and distributed applications rely on hashing algorithms that allow dynamic scaling of a robust and efficient hash table. Examples include AWS, Google Cloud and BitTorrent. Consistent and rendezvous hashing are algorithms…

Quantum mechanical calculations for material modelling using Kohn-Sham density functional theory (DFT) involve the solution of a nonlinear eigenvalue problem for $N$ smallest eigenvector-eigenvalue pairs with $N$ proportional to the number…

We propose a Hermite spectral method for the inelastic Boltzmann equation, which makes two-dimensional periodic problem computation affordable by the hardware nowadays. The new algorithm is based on a Hermite expansion, where the expansion…

The real-space density-functional perturbation theory (DFPT) for the computations of the response properties with respect to the atomic displacement and homogeneous electric field perturbation has been recently developed and implemented…

We describe a quantum algorithm for finding the smallest eigenvalue of a Hermitian matrix. This algorithm combines Quantum Phase Estimation and Quantum Amplitude Estimation to achieve a quadratic speedup with respect to the best classical…

Finite-element (FE) discretisations have emerged as a powerful real-space alternative to large-scale Kohn-Sham density functional theory (DFT) calculations, offering systematic convergence, excellent parallel scalability, while…

The accuracy and effectiveness of Hermite spectral methods for the numerical discretization of partial differential equations on unbounded domains, are strongly affected by the amplitude of the Gaussian weight function employed to describe…

In this work, we consider the solution of boundary integral equations by means of a scalable hierarchical matrix approach on clusters equipped with graphics hardware, i.e. graphics processing units (GPUs). To this end, we extend our…

In this article, we establish a class of new accelerated modulus-based iteration methods for solving the linear complementarity problem. When the system matrix is an $H_+$-matrix, we present appropriate criteria for the convergence…

One of the main computational bottlenecks when working with kernel based learning is dealing with the large and typically dense kernel matrix. Techniques dealing with fast approximations of the matrix vector product for these kernel…

Nowadays, we are to find out solutions to huge computing problems very rapidly. It brings the idea of parallel computing in which several machines or processors work cooperatively for computational tasks. In the past decades, there are a…

Laplacian eigenmap algorithm is a typical nonlinear model for dimensionality reduction in classical machine learning. We propose an efficient quantum Laplacian eigenmap algorithm to exponentially speed up the original counterparts. In our…

This paper presents a parallel algorithm for finding the smallest eigenvalue of a particular form of ill-conditioned Hankel matrix, which requires the use of extremely high precision arithmetic. Surprisingly, we find that commonly-used…

To solve non-Hermitian linear system Ax=b on parallel and vector machines, some paralell multisplitting methods are considered. In this work, in particular: i) We establish the convergence results of the paralell multisplitting methods,…

PHAST is a software package written in standard Fortran, with MPI and CUDA extensions, able to efficiently perform parallel multicanonical Monte Carlo simulations of single or multiple heteropolymeric chains, as coarse-grained models for…

We consider an approximate computation of several minimal eigenpairs of large Hermitian matrices which come from high--dimensional problems. We use the tensor train format (TT) for vectors and matrices to overcome the curse of…

As supercomputers become larger with powerful Graphics Processing Unit (GPU), traditional direct eigensolvers struggle to keep up with the hardware evolution and scale efficiently due to communication and synchronization demands.…