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Littérature scientifique sur le sujet « Rank-one Laplacian »

Auteur : Grafiati

Publié le 2 juin 2025

Mis à jour le 31 juillet 2025

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Articles de revues sur le sujet "Rank-one Laplacian"

Conejero, J. Alberto, Antonio Falcó, and María Mora–Jiménez. "A pre-processing procedure for the implementation of the greedy rank-one algorithm to solve high-dimensional linear systems." AIMS Mathematics 8, no. 11 (2023): 25633–53. http://dx.doi.org/10.3934/math.20231308.

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<abstract><p>Algorithms that use tensor decompositions are widely used due to how well they perfor with large amounts of data. Among them, we find the algorithms that search for the solution of a linear system in separated form, where the greedy rank-one update method stands out, to be the starting point of the famous proper generalized decomposition family. When the matrices of these systems have a particular structure, called a Laplacian-like matrix which is related to the aspect of the Laplacian operator, the convergence of the previous method is faster and more accurate. The ma

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Lakaev, Sh S., O. I. Kurbonov, and V. U. Aktamova. "Threshold Analysis of the One-Rank Perturbation Non-Local Discrete Laplacian." Lobachevskii Journal of Mathematics 43, no. 8 (2022): 2187–93. http://dx.doi.org/10.1134/s1995080222110178.

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JI, LIZHEN, and ANDREAS WEBER. "The spectrum and heat dynamics of locally symmetric spaces of higher rank." Ergodic Theory and Dynamical Systems 35, no. 5 (2014): 1524–45. http://dx.doi.org/10.1017/etds.2014.3.

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The aim of this paper is to study the spectrum of the$L^{p}$Laplacian and the dynamics of the$L^{p}$heat semigroup on non-compact locally symmetric spaces of higher rank. Our work here generalizes previously obtained results in the setting of locally symmetric spaces of rank one to higher rank spaces. Similarly as in the rank-one case, it turns out that the$L^{p}$heat semigroup on$M$has a certain chaotic behavior if$p\in (1,2)$, whereas for$p\geq 2$such chaotic behavior never occurs.

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Tyrtyshnikov, Eugene E. "Tensor decompositions and rank increment conjecture." Russian Journal of Numerical Analysis and Mathematical Modelling 35, no. 4 (2020): 239–46. http://dx.doi.org/10.1515/rnam-2020-0020.

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AbstractSome properties of tensor ranks and the non-closeness issue of sets with given restrictions on the rank of tensors entering those sets are studied. It is proved that the rank of the d-dimensional Laplacian equals d. The following conjecture is formulated: for any tensor of non-maximal rank there exists a nonzero decomposable tensor (tensor of rank 1) such that the rank increases by one after adding this tensor. In the general case, it is proved that this property holds algebraically almost everywhere for complex tensors of fixed size whose rank is strictly less than the generic rank.

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So, Wasin. "Rank one perturbation and its application to the laplacian spectrum of a graph∗." Linear and Multilinear Algebra 46, no. 3 (1999): 193–98. http://dx.doi.org/10.1080/03081089908818613.

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Hilgert, J., A. Pasquale, and T. Przebinda. "Resonances for the Laplacian on products of two rank one Riemannian symmetric spaces." Journal of Functional Analysis 272, no. 4 (2017): 1477–523. http://dx.doi.org/10.1016/j.jfa.2016.12.009.

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Xu, Zhixuan, Caikou Chen, Guojiang Han, and Jun Gao. "Robust subspace clustering based on latent low rank representation with non-negative sparse Laplacian constraints." Journal of Intelligent & Fuzzy Systems 40, no. 6 (2021): 12151–65. http://dx.doi.org/10.3233/jifs-210274.

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As a successful improvement on Low Rank Representation (LRR), Latent Low Rank Representation (LatLRR) has been one of the state-of-the-art models for subspace clustering due to the capability of discovering the low dimensional subspace structures of data, especially when the data samples are insufficient and/or extremely corrupted. However, the LatLRR method does not consider the nonlinear geometric structures within data, which leads to the loss of the locality information among data in the learning phase. Moreover, the coefficients of the learnt representation matrix can be negative, which l

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Ge, Shuguang, Xuesong Wang, Yuhu Cheng, and Jian Liu. "Cancer Subtype Recognition Based on Laplacian Rank Constrained Multiview Clustering." Genes 12, no. 4 (2021): 526. http://dx.doi.org/10.3390/genes12040526.

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Integrating multigenomic data to recognize cancer subtype is an important task in bioinformatics. In recent years, some multiview clustering algorithms have been proposed and applied to identify cancer subtype. However, these clustering algorithms ignore that each data contributes differently to the clustering results during the fusion process, and they require additional clustering steps to generate the final labels. In this paper, a new one-step method for cancer subtype recognition based on graph learning framework is designed, called Laplacian Rank Constrained Multiview Clustering (LRCMC).

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Jeyaraman, I., T. Divyadevi, and R. Azhagendran. "The Moore-Penrose inverse of the distance matrix of a helm graph." Electronic Journal of Linear Algebra 39 (March 23, 2023): 94–109. http://dx.doi.org/10.13001/ela.2023.7465.

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In this paper, we give necessary and sufficient conditions for a real symmetric matrix and, in particular, for the distance matrix $D(H_n)$ of a helm graph $H_n$ to have their Moore-Penrose inverses as the sum of a symmetric Laplacian-like matrix and a rank-one matrix. As a consequence, we present a short proof of the inverse formula, given by Goel (Linear Algebra Appl. 621:86-104, 2021), for $D(H_n)$ when $n$ is even. Further, we derive a formula for the Moore-Penrose inverse of singular $D(H_n)$ that is analogous to the formula for $D(H_n)^{-1}$. Precisely, if $n$ is odd, we find a symmetric

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Awonusika, Richard, and Ali Taheri. "A Spectral Identity on Jacobi Polynomials and its Analytic Implications." Canadian Mathematical Bulletin 61, no. 3 (2018): 473–82. http://dx.doi.org/10.4153/cmb-2017-056-8.

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AbstractThe Jacobi coefficientsare linked to the Maclaurin spectral expansion of the Schwartz kernel of functions of the Laplacian on a compact rank one symmetric space. It is proved that these coefficients can be computed by transforming the even derivatives of the Jacobi polynomialsinto a spectral sum associated with the Jacobi operator. The first few coefficients are explicitly computed, and a direct trace interpretation of the Maclaurin coefficients is presented.

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Thèses sur le sujet "Rank-one Laplacian"

Newman, Adam. "Behaviour of eigenfunction subsequences for delta-perturbed 2D quantum systems." Thesis, Loughborough University, 2016. https://dspace.lboro.ac.uk/2134/21568.

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We consider a quantum system whose unperturbed form consists of a self-adjoint Δ-operator on a 2-dimensional compact Riemannian manifold, which may or may not have a boundary. Then as a perturbation, we add a delta potential/point scatterer at some select point ρ. The perturbed self-adjoint operator is constructed rigorously by means of self-adjoint extension theory. We also consider a corresponding classical dynamical system on the cotangent/cosphere bundle, consisting of geodesic flow on the manifold, with specular reflection if there is a boundary. Chapter 2 describes the mathematics of the

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