Related papers: On Eigenvector Computation and Eigenvalue Reorderi…

Bilevel optimization offers a methodology to learn hyperparameters in imaging inverse problems, yet its integration with automatic differentiation techniques remains challenging. On the one hand, inverse problems are typically solved by…

Deploying deep neural networks on edge devices is often limited by the memory traffic and compute cost of dense linear operators. While quaternion neural networks improve parameter efficiency by coupling multiple channels through Hamilton…

The aim of this paper is to develop an algebraic multigrid method to solve eigenvalue problems based on the combination of the multilevel correction scheme and the algebraic multigrid method for linear equations. Our approach uses the…

In this paper, we study an adaptive finite element method for multiple eigenvalue problems of a class of second order elliptic equations. By using some eigenspace approximation technology and its crucial property which is also presented in…

This article considers the problem of designing adaption and optimisation techniques for training quantum learning machines. To this end, the division algebra of quaternions is used to derive an effective model for representing computation…

Higher-order singular value decomposition (HOSVD) is one of the most efficient tensor decomposition techniques. It has the salient ability to represent high_dimensional data and extract features. In more recent years, the quaternion has…

All quaternion methods for static attitude determination currently rely on either the spectral decomposition of a 4 x 4 matrix (q-Method) or finding the maximum eigenvalue of a 4th-order characteristic equation (QUEST). Using a spectral…

A novel approach is given to overcome the computational challenges of the full-matrix Adaptive Gradient algorithm (Full AdaGrad) in stochastic optimization. By developing a recursive method that estimates the inverse of the square root of…

We develop a method to search for the optimal code space, induced decay rates and control Hamiltonian to implement autonomous quantum error correction (AQEC) for a general open quantum system. The system is defined by a free-evolution…

We present SPEC-RE, a new algorithm to sort complex eigenvalues, generated as the solutions to algebraic equations, whose coefficients are analytic functions of one or many, possibly complex parameters. The fact that the eigenvalues are…

In this paper, we discuss the solution of a Quadratic Eigenvalue Complementarity Problem (QEiCP) by using Difference of Convex (DC) programming approaches. We first show that QEiCP can be represented as dc programming problem. Then we…

The eigenvalue shift technique is the most well-known and fundamental tool for matrix computations. Applications include the search of eigeninformation, the acceleration of numerical algorithms, the study of Google's PageRank. The shift…

There has been growing interest in high-order tensor methods for nonconvex optimization, with adaptive regularization, as they possess better/optimal worst-case evaluation complexity globally and faster convergence asymptotically. These…

In this paper, we propose a spectral framework that embeds 1D and 2D quasiperiodic Helmholtz eigenvalue problems into higher-dimensional (2D and 4D) periodic spaces via the projection method \cite{jiang2014numerical, jiang2024numerical}. To…

We propose a quantum algorithm for finding eigenvalues of non-unitary matrices. We show how to construct, through interactions in a quantum system and projective measurements, a non-Hermitian or non-unitary matrix and obtain its eigenvalues…

The implicitly shifted QR iteration is used as a restart procedure for the Arnoldi method for the calculation of a few dominant eigenvalues of a large matrix. We show that the underlying idea of implicit polynomial filtering can be utilized…

The learning process for multi layered neural networks with many nodes makes heavy demands on computational resources. In some neural network models, the learning formulas, such as the Widrow-Hoff formula, do not change the eigenvectors of…

In this paper we briefly outline the quadrature method for estimating uncertainties in a function of several variables and apply it to estimate the numerical uncertainties in QCD-QED rescaling factors. We employ here the one-loop order in…

The generalized eigenvalue (GE) problems are of particular importance in various areas of science engineering and machine learning. We present a variational quantum algorithm for finding the desired generalized eigenvalue of the GE problem,…

This paper presents a method for computing eigenvalues and eigenvectors for some types of nonlinear eigenvalue problems. The main idea is to approximate the functions involved in the eigenvalue problem by rational functions and then apply a…