2024 Splitting methods for tensor equations

Splitting methods for tensor equations

Author: oyrq

August undefined, 2024

Web9 Sep 2024 · Based on the weak regular splitting of tensors, preconditioned technology has shown great advantages in solving tensor equations with nonsingular (strong) ℳ … WebWe study an elliptic equation with stochastic coefficient modeled as a lognormal random field. A perturbation approach is adopted, expanding the solution in Ta 掌桥科研一站式科研服务平台

Developing iterative algorithms to solve Sylvester tensor equations …

Web15 Nov 2024 · For any given tensor X ∈ R n 1 × n 2 × ⋯ × n m and matrix A ∈ R p × n k, their k -mode product, denoted by X × k A, is an m th order n 1 × ⋯ × n k − 1 × p × n k + 1 × ⋯ × n m dimensional tensor whose entries are given by ( X × k A) i 1 ⋯ i k − 1 j i k + 1 ⋯ i m = ∑ i k = 1 n k x i 1 ⋯ i k ⋯ i m a j i k, j = 1, ⋯, p. Web14 Jul 2024 · In this paper, two attractive iterative methods – conjugate gradient squared (CGS) and conjugate residual squared (CRS) – are extended to solve the generalized coupled Sylvester tensor equations ∑ j = 1 n X j × 1 A ij 1 × 2 A ij 2... × d A ijd = C i, i = 1, 2,..., n. The proposed methods use tensor computations with no maricizations involved. tim guthrie come to scilly

Preconditioned tensor splitting AOR iterative methods for …

Web27 Feb 2024 · In this paper, a tensor splitting AOR iterative method for solving the H+-tensor absolute value equation is presented. Some sufficient conditions for the existence of the … Web1 Apr 2024 · Splitting methods for tensor equations: LI et al . DOI: Authors: Dong-Hui Li Xie Shuilian Jiaying University Hongru Xu Jiaying University Abstract The Jacobi, Gauss … Web22 Sep 2024 · We consider both stand and accelerated tensor splitting methods for solving the reformulated fixed-point equations of tensor complementarity problems. The … tim guthrie arlington baptist church

Hermitian and skew-Hermitian splitting methods for …

1, Yajun Xie 2,* and Jie Yao 2 - ResearchGate

Web1 Apr 2024 · By introducing certain auxiliary variables, we transform equivalently this tensor equation into a consensus constrained optimization problem, and then propose an ADMM type method for it. It turns out that each limit point of the sequences generated by this method satisfies the Karush-Kuhn-Tucker conditions. Web1 Sep 2024 · In this paper, we verify the existence of solutions of tensor absolute value equations and propose the tensor splitting methods for solving this class of equation. … tim guthrie creightonWeb15 Feb 2024 · Efficient Splitting Methods for Solving Tensor Absolute Value Equation 1. Introduction. Symbol ‘ ’ denotes a matrix-tensor product (see details in the next section). … tim gunn shows

"Web11 Apr 2024 · The hierarchical equations of motion (HEOM) method is a numerically exact open quantum system dynamics approach. The method is rooted in an exponential expansion of the bath correlation function, which in essence strategically reshapes a continuous environment into a set of effective bath modes that allow for more efficient … " - Splitting methods for tensor equations

Splitting methods for tensor equations

Preconditioned tensor splitting AOR iterative methods for …

Web5 Jun 2024 · In this note, we present three efficient operator-splitting methods for the convex co-clustering problem: a standard two-block ADMM, a Generalized ADMM which avoids an expensive tensor Sylvester equation in the primal update, and a three-block ADMM based on the operator splitting scheme of Davis and Yin. Web24 Jun 2024 · The method combines functional tensor train (FTT) series expansions, operator splitting time integration, and a new rank-adaptive algorithm based on a thresholding criterion that limits the component of the PDE velocity vector normal to the FTT tensor manifold.

Did you know?

Web9 Sep 2024 · Based on the weak regular splitting of tensors, preconditioned technology has shown great advantages in solving tensor equations with nonsingular (strong) ℳ …

Web15 Feb 2024 · Based on the weak regular splitting of tensors, preconditioned technology has shown great advantages in solving tensor equations with nonsingular (strong) ℳ‐tensors. … Websplitting methods for solving this class of equation. Furthermore, the convergence analysis of the tensor splitting method is also studied under suitable conditions. Finally, numerical …

Webmethod (AOR) (called TAOR) for solving tensor absolute value equations. Furthermore, one type of preconditioned tensor splitting method is also applied for solving structured … Web15 Oct 2024 · We first propose the regular sketch-and-project method for solving tensor equations with respect to the popular t-product. Then, three adaptive sampling strategies and three corresponding adaptive sketch-and-project methods are derived. We prove that all the proposed methods have linear convergence in expectation. Furthermore, we …

Web11 Jun 2024 · A Tensor Splitting AOR Iterative Method for Solving a Tensor Absolute Value Equation Yuhan Chen, Chenliang Li Mathematics Mathematics 2024 In this paper, a tensor splitting AOR iterative method for solving the H+-tensor absolute value equation is presented. Some sufficient conditions for the existence of the solution to the tensor…

Web1 Dec 2024 · [1] Let A ∈ T ( m, n) and I ∈ T ( m, n) be a unit tensor. If A I = 0, then A = 0. Definition 2.6 [11] Let A ∈ T ( m, n). If M ( A) is a nonsingular matrix and A = M ( A) I, then A is called left-invertible or left-nonsingular, M ( A) − 1 is called the order 2 left-inverse of A. parking near 1 south dearbornWebFirstly, we extend the Hermitian and skew-Hermitian splitting (HSS) method to solve the tensor equation. Then we propose a new Hermitian splitting (NHS) method under some … parking near 200 central park westWeb30 Nov 2024 · In this paper, we study the solution method of tensor complementarity problem. Based on the equivalence relation of the tensor complementarity problem and unconstrained optimization problem, we propose a new smoothing spectral conjugate gradient method with Armijo line search. Under mild conditions, we establish the global … parking near 1 mill street leamingtonWeb14 Apr 2024 · Cancer is a leading cause of death across the globe, in which lung cancer constitutes the maximum mortality rate. Early diagnosis through computed tomography scan imaging helps to identify the stages of lung cancer. Several deep learning–based classification methods have been employed for developing automatic systems for the … tim gurner wikipediaWebFirstly, we extend the Hermitian and skew-Hermitian splitting (HSS) method to solve the tensor equation. Then we propose a new Hermitian splitting (NHS) method under some certain conditions, which is expected to converge faster than the HSS iteration. We also present the optimal parameters of both the HSS and NHS methods. tim guthrie excursionsWeb29 May 2024 · We first extend the accelerated overrelaxation (AOR) splitting method to solve the tensor equation. To improve the convergence, we develop a Newton-AOR … parking near 219 s dearborn chicagoWeb9 Sep 2024 · A Tensor Splitting AOR Iterative Method for Solving a Tensor Absolute Value Equation. In this paper, a tensor splitting AOR iterative method for solving the H+-tensor … parking near 200 s grand ave los angeles ca