Related papers: A Multilevel Spectral Indicator Method for Eigenva…

Hidden Markov models have successfully been applied as models of discrete time series in many fields. Often, when applied in practice, the parameters of these models have to be estimated. The currently predominating identification methods,…

Studying the optoelectronic structure of materials can require the computation of several thousands of the smallest positive eigenpairs of a pseudo-hermitian Hamiltonian. Iterative eigensolvers may be preferred over direct methods for this…

We present spectral analysis modal methods (SAMMs) to perform POD in the frequency domain using non-time-resolved Particle Image Velocity (PIV) data combined with unsteady surface pressure measurements. In particular, time-resolved unsteady…

Stacked intelligent metasurfaces (SIMs) facilitate computation by cascaded programmable layers so that part of the signal processing can be performed in the wave domain during signal propagation, rather than solely after reception. This…

We describe a randomized Krylov-subspace method for estimating the spectral condition number of a real matrix A or indicating that it is numerically rank deficient. The main difficulty in estimating the condition number is the estimation of…

Among super-resolution microscopy techniques, structured illumination microscopy (SIM) shows great advances of low phototoxicity, high speed, and excellent performance in long-term dynamic observation, making it especially suitable for live…

In many areas of machine learning, it becomes necessary to find the eigenvector decompositions of large matrices. We discuss two methods for reducing the computational burden of spectral decompositions: the more venerable Nystom extension…

Structured Illumination Microscopy (SIM) enables rapid, high-contrast optical sectioning of fresh tissue without staining or physical sectioning, making it promising for intraoperative and point-of-care diagnostics. Recent foundation and…

Hyperspectral images often have hundreds of spectral bands of different wavelengths captured by aircraft or satellites that record land coverage. Identifying detailed classes of pixels becomes feasible due to the enhancement in spectral and…

Denoising is a crucial step for hyperspectral image (HSI) applications. Though witnessing the great power of deep learning, existing HSI denoising methods suffer from limitations in capturing the non-local self-similarity. Transformers have…

The Asymptotic Iteration Method (AIM) is a technique for solving analytically and approximately the linear second-order differential equation, especially the eigenvalue problems that frequently appear in theoretical and mathematical…

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…

We propose a wave operator method to calculate eigenvalues and eigenvectors of large parameter-dependent matrices, using an adaptative active subspace. We consider a hamiltonian which depends on external adjustable or adiabatic parameters,…

Chaotic behavior or lack thereof in non-Hermitian systems is often diagnosed via spectral analysis of associated complex eigenvalues. Very recently, singular values of the associated non-Hermitian systems have been proposed as an effective…

Computing eigenvalues of very large matrices is a critical task in many machine learning applications, including the evaluation of log-determinants, the trace of matrix functions, and other important metrics. As datasets continue to grow in…

Regularization is essential in deep learning to enhance generalization and mitigate overfitting. However, conventional techniques often rely on heuristics, making them less reliable or effective across diverse settings. We propose Self…

Randomized block Krylov subspace methods form a powerful class of algorithms for computing the extreme eigenvalues of a symmetric matrix or the extreme singular values of a general matrix. The purpose of this paper is to develop new…

In this work, we are interested in solving large linear systems stemming from the Extra-Membrane-Intra (EMI) model, which is employed for simulating excitable tissues at a cellular scale. After setting the related systems of partial…

This paper proposes a novel method for segmentation of images by hierarchical multilevel thresholding. The method is global, agglomerative in nature and disregards pixel locations. It involves the optimization of the ratio of the unbiased…

We develop an iterative refinement method that improves the accuracy of a user-chosen subset of $k$ eigenvectors ($k\ll n$) of an $n\times n$ real symmetric matrix. Using an orthogonal matrix represented in compact WY form, the method…