A two-step accelerated Levenberg-Marquardt method for solving multilinear systems in tensor-train format

DOI10.1016/j.cam.2020.113069zbMath1442.65042OpenAlexW3037057771MaRDI QIDQ2196036

Yu-Tao Zheng, Bing Zheng, Ruijuan Zhao, Mao-Lin Liang

Publication date: 28 August 2020

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2020.113069

zbMATH Keywords

Levenberg-Marquardt methodtensor-train formatmultilinear systemsTALM method

Mathematics Subject Classification ID

Iterative numerical methods for linear systems (65F10) Multilinear algebra, tensor calculus (15A69) Linear equations (linear algebraic aspects) (15A06)

Uses Software

• TensorToolbox
• TT Toolbox
• GitHub

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Tensor Decompositions and Applications
• Tensor-Train Decomposition
• The sparsest solutions to \(Z\)-tensor complementarity problems
• The tensor splitting with application to solve multi-linear systems
• A Levenberg-Marquardt method for solving semi-symmetric tensor equations
• Alternating iterative methods for solving tensor equations with applications
• A globally and quadratically convergent algorithm for solving multilinear systems with \(\mathcal {M}\)-tensors
• On the convergence of the modified Levenberg-Marquardt method with a nonmonotone second order Armijo type line search
• Incremental numerical recipes for the high efficient inversion of the confluent Vandermonde matrices
• A new scheme for the tensor representation
• Preconditioned tensor splitting iterations method for solving multi-linear systems
• Solving sparse non-negative tensor equations: algorithms and applications
• Solving multi-linear systems with \(\mathcal {M}\)-tensors
• A homotopy method for solving multilinear systems with M-tensors
• A literature survey of low-rank tensor approximation techniques
• The Alternating Linear Scheme for Tensor Optimization in the Tensor Train Format
• Alternating Minimal Energy Methods for Linear Systems in Higher Dimensions
• Hierarchical Singular Value Decomposition of Tensors
• The modified Levenberg-Marquardt method for nonlinear equations with cubic convergence
• High Order Bellman Equations and Weakly Chained Diagonally Dominant Tensors
• Breaking the Curse of Dimensionality, Or How to Use SVD in Many Dimensions
• Exact solutions for the nonlinear Klein–Gordon and Liouville equations in four-dimensional Euclidean space
• An Algorithm for Least-Squares Estimation of Nonlinear Parameters
• A Curvilinear Search Using Tridiagonal Secant Updates for Unconstrained Optimization
• Fourth-Order Cumulant-Based Blind Identification of Underdetermined Mixtures
• Splitting methods for tensor equations
• An efficient Levenberg–Marquardt method with a new LM parameter for systems of nonlinear equations
• Fast Solution of Parabolic Problems in the Tensor Train/Quantized Tensor Train Format with Initial Application to the Fokker--Planck Equation
• Klein‐Gordon‐Zakharov system in energy space: Blow‐up profile and subsonic limit
• Tensor Analysis
• A projection method to solve linear systems in tensor format
• Accelerating the modified Levenberg-Marquardt method for nonlinear equations
• Numerical approach to the non-linear diofantic equations with applications to the controllability of infinite dimensional dynamical systems
• Higher Order Positive Semidefinite Diffusion Tensor Imaging
• A method for the solution of certain non-linear problems in least squares

This page was built for publication: A two-step accelerated Levenberg-Marquardt method for solving multilinear systems in tensor-train format