Related papers: Iterative Methods for Computing Eigenvalues and Ei…

The capacity for solving eigenstates with a quantum computer is key for ultimately simulating physical systems. Here we propose inverse iteration quantum eigensolvers, which exploit the power of quantum computing for the classical inverse…

One way to study an hypergraph is to attach to it a tensor. Tensors are a generalization of matrices, and they are an efficient way to encode information in a compact form. In this paper we study how properties of weighted hypergraphs are…

We develop an efficient algorithm for sampling the eigenvalues of random matrices distributed according to the Haar measure over the orthogonal or unitary group. Our technique samples directly a factorization of the Hessenberg form of such…

Waveguide and resonant properties of diffractive structures are often explained through the complex poles of their scattering matrices. Numerical methods for calculating poles of the scattering matrix with applications in grating theory are…

This paper introduces a method for computing eigenvalues and eigenvectors of a generalized Hermitian, matrix eigenvalue problem. The work is focused on large scale eigenvalue problems, where the application of a direct inverse is out of…

We present a practical Newton-based method for computing left eigenvalues of quaternion matrices. It uses only standard real/complex linear-algebra kernels via embeddings and applies to matrices of any size. Extensive tests on literature…

We propose a characterization of a $p$-Laplace higher eigenvalue based on the inverse iteration method with balancing the Rayleigh quotients of the positive and negative parts of solutions to consecutive $p$-Poisson equations. The approach…

EigenDecomposition (ED) is at the heart of many computer vision algorithms and applications. One crucial bottleneck limiting its usage is the expensive computation cost, particularly for a mini-batch of matrices in the deep neural networks.…

The QR-algorithm is one of the most important algorithms in linear algebra. Its several variants make feasible the computation of the eigenvalues and eigenvectors of a numerical real or complex matrix, even when the dimensions of the matrix…

An iterative method we previously proposed to compute nuclear strength functions is developed to allow it to accurately calculate properties of individual nuclear states. The approach is based on the quasi-particle-random-phase…

We explore an algorithm for approximating roots of integers, discuss its motivation and derivation, and analyze its convergence rates with varying parameters and inputs. We also perform comparisons with established methods for approximating…

The polynomial eigenvalue problem arises in many applications and has received a great deal of attention over the last decade. The use of root-finding methods to solve the polynomial eigenvalue problem dates back to the work of…

Affine iterations of the form x(n+1) = Ax(n) + b converge, using real arithmetic, if the spectral radius of the matrix A is less than 1. However, substituting interval arithmetic to real arithmetic may lead to divergence of these…

Permutations can be represented as linear combinations of natural numbers with different powers. In this paper, its coefficient matrix and inverse matrix is derived, and the results show the coefficient matrix is a lower triangular matrix…

This article is a brief introduction to quantum algorithms for the eigenvalue problem in quantum many-body systems. Rather than a broad survey of topics, we focus on providing a conceptual understanding of several quantum algorithms that…

The matrix factor model has drawn growing attention for its advantage in achieving two-directional dimension reduction simultaneously for matrix-structured observations. In this paper, we propose a simple iterative least squares algorithm…

In this article we provide a fast computational method in order to calculate the Moore-Penrose inverse of singular square matrices and of rectangular matrices. The proposed method proves to be much faster and has significantly better…

This paper presents a Jacobi-type iteration for computing a given specified eigenpair of a symmetric matrix. For a certain class of diagonally dominant matrices, the procedure is shown to converge at a linear rate depending on how the…

This paper investigates the eigenvalue computation problem of the dual quaternion Hermitian matrix closely related to multi-agent group control. Recently, power method was proposed by Cui and Qi in Journal of Scientific Computing, 100…

The tensor t-product, introduced by Kilmer and Martin [26], is a powerful tool for the analysis of and computation with third-order tensors. This paper introduces eigentubes and eigenslices of third-order tensors under the t-product. The…