相关论文: A New Highly Parallel Non-Hermitian Eigensolver
Interior eigenvalue problems for large-scale sparse Hermitian matrices are fundamental in computational science. We propose an adaptive polynomial filtering strategy based on Chebyshev expansion of a step function, integrated into a…
Estimating the number of eigenvalues located in a given interval of a large sparse Hermitian matrix is an important problem in certain applications and it is a prerequisite of eigensolvers based on a divide-and-conquer paradigm. Often an…
The matrix element method utilizes ab initio calculations of probability densities as powerful discriminants for processes of interest in experimental particle physics. The method has already been used successfully at previous and current…
An efficient algorithm for computing eigenvectors of a matrix of integers by exact computation is proposed. The components of calculated eigenvectors are expressed as polynomials in the eigenvalue to which the eigenvector is associated, as…
The eigenvalue density of a matrix plays an important role in various types of scientific computing such as electronic-structure calculations. In this paper, we propose a quantum algorithm for computing the eigenvalue density in a given…
The existing doubling algorithms have been proven efficient for several important nonlinear matrix equations arising from real-world engineering applications. In a nutshell, the algorithms iteratively compute a basis matrix, in one of the…
We report an efficient program for computing the eigenvalues and symmetry-adapted eigenvectors of very large quaternionic (or Hermitian skew-Hamiltonian) matrices, using which structure-preserving diagonalization of matrices of dimension N…
The Hessian matrix has a number of important applications in a variety of different fields, such as optimzation, image processing and statistics. In this paper we focus on the practical aspects of efficiently computing Hessian matrices in…
In this work, we consider a rational approximation of the exponential function to design an algorithm for computing matrix exponential in the Hermitian case. Using partial fraction decomposition, we obtain a parallelizable method, where the…
We present an iterative algorithm for computing an invariant subspace associated with the algebraically smallest eigenvalues of a large sparse or structured Hermitian matrix A. We are interested in the case in which the dimension of the…
In this paper we describe HeSP, a complete simulation framework to study a general task scheduling-partitioning problem on heterogeneous architectures, which treats recursive task partitioning and scheduling decisions on equal footing.…
This paper proposes an efficient method for computing selected generalized eigenpairs of a sparse Hermitian definite matrix pencil $(A,B)$. Based on Zolotarev's best rational function approximations of the signum function and conformal…
The program FIESTA has been completely rewritten. Now it can be used not only as a tool to evaluate Feynman integrals numerically, but also to expand Feynman integrals automatically in limits of momenta and masses with the use of sector…
Matrix powering is a fundamental computational primitive in linear algebra. It has widespread applications in scientific computing and engineering, and underlies the solution of time-homogeneous linear ordinary differential equations,…
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.…
Hermite interpolation property is desired in applied and computational mathematics. Hermite and vector subdivision schemes are of interest in CAGD for generating subdivision curves and in computational mathematics for building Hermite…
Pseudo-hermitian matrices are matrices hermitian with respect to an indefinite metric. They can be thought of as the truncation of pseudo-hermitian operators, defined over some Krein space, together with the associated metric, to a finite…
Such problems as computation of spectra of spin chains and vibrational spectra of molecules can be written as high-dimensional eigenvalue problems, i.e., when the eigenvector can be naturally represented as a multidimensional tensor. Tensor…
We study fast algorithms for computing fundamental properties of a positive semidefinite kernel matrix $K \in \mathbb{R}^{n \times n}$ corresponding to $n$ points $x_1,\ldots,x_n \in \mathbb{R}^d$. In particular, we consider estimating the…
A novel parallel hybrid quantum-classical algorithm for the solution of the quantum-chemical ground-state energy problem on gate-based quantum computers is presented. This approach is based on the reduced density-matrix functional theory…