Related papers: Non-linear eigensolver-based alternative to tradit…
The linear FEAST algorithm is a method for solving linear eigenvalue problems. It uses complex contour integration to calculate the eigenvectors whose eigenvalues that are located inside some user-defined region in the complex plane. This…
A detailed new upgrade of the FEAST eigensolver targeting non-Hermitian eigenvalue problems is presented and thoroughly discussed. It aims at broadening the class of eigenproblems that can be addressed within the framework of the FEAST…
A new numerical algorithm for solving the symmetric eigenvalue problem is presented. The technique deviates fundamentally from the traditional Krylov subspace iteration based techniques (Arnoldi and Lanczos algorithms) or other…
In a recent article [1], the FEAST algorithm has been presented as a general purpose eigenvalue solver which is ideally suited for addressing the numerical challenges in electronic structure calculations. Here, FEAST is presented beyond the…
The FEAST algorithm is a subspace iteration method that uses a spectral projector as a rational filter in order to efficiently solve interior eigenvalue problems in parallel. Although the solutions from the FEAST algorithm converge rapidly…
The FEAST algorithm, due to Polizzi, is a typical contour-integral based eigensolver for computing the eigenvalues, along with their eigenvectors, inside a given region in the complex plane. It was formulated under the circumstance that the…
Calculating portions of eigenvalues and eigenvectors of matrices or matrix pencils has many applications. An approach to this calculation for Hermitian problems based on a density matrix has been proposed in 2009 and a software package…
Iterative multiscale methods for electronic structure calculations offer several advantages for large-scale problems. Here we examine a nonlinear full approximation scheme (FAS) multigrid method for solving fixed potential and…
The contour-integral based eigensolvers are the recent efforts for computing the eigenvalues inside a given region in the complex plane. The best-known members are the Sakurai-Sugiura (SS) method, its stable version CIRR, and the FEAST…
Solving the Kohn-Sham eigenvalue problem constitutes the most computationally expensive part in self-consistent density functional theory (DFT) calculations. In a previous paper, we have proposed a nonlinear Chebyshev-filtered subspace…
We present an efficient computational approach to perform real-space electronic structure calculations using an adaptive higher-order finite-element discretization of Kohn-Sham density-functional theory (DFT). To this end, we develop an…
Contour integration techniques have become a popular choice for solving the linear and non-linear eigenvalue problems. They principally include the Sakurai-Sugiura methods, the Beyn's algorithm, the FEAST/NLFEAST algorithms and other…
The calculation of a segment of eigenvalues and their corresponding eigenvectors of a Hermitian matrix or matrix pencil has many applications. A new density-matrix-based algorithm has been proposed recently and a software package FEAST has…
The quantum mechanical ground state of electrons is described by Density Functional Theory, which leads to large minimization problems. An efficient minimization method uses a selfconsistent field (SCF) solution of large eigenvalue…
A parallel implementation of an eigensolver designed for electronic structure calculations is presented. The method is applicable to computational tasks that solve a sequence of eigenvalue problems where the solution for a particular…
We propose an adaptive planewave method for eigenvalue problems in electronic structure calculations. The method combines a priori convergence rates and accurate a posteriori error estimates into an effective way of updating the energy…
An operator analogue of the FEAST matrix eigensolver is developed to compute the discrete part of the spectrum of a differential operator in a region of interest in the complex plane. Unbounded search regions are handled with a novel…
The FEAST library package represents an unified framework for solving various family of eigenvalue problems and achieving accuracy, robustness, high-performance and scalability on parallel architectures. Its originality lies with a new…
Recently J. M. Arrazola et al. [Phys. Rev. A 100, 032306 (2019)] proposed a quantum algorithm for solving nonhomogeneous linear partial differential equations of the form $A\psi(\textbf{r})=f(\textbf{r})$. Its nonhomogeneous solution is…
We develop and analyze a fault-tolerant quantum algorithm for computing $n$-th order response properties necessary for analysis of non-linear spectroscopies of molecular and condensed phase systems. We use a semi-classical description in…