scholarly journals A Dynamically Adjusted Subspace Gradient Method and Its Application in Image Restoration

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2450
Author(s):  
Jun Huo ◽  
Yuping Wu ◽  
Guoen Xia ◽  
Shengwei Yao
Keyword(s):  
Image Restoration ◽  
Gradient Method ◽  
Symmetric Matrix ◽  
Hessian Matrix ◽  
Three Dimensional ◽  
Linear Convergence ◽  
Dimensional Subspace ◽  
Search Direction ◽  
Quadratic Model ◽  
Numerical Performance

In this paper, a new subspace gradient method is proposed in which the search direction is determined by solving an approximate quadratic model in which a simple symmetric matrix is used to estimate the Hessian matrix in a three-dimensional subspace. The obtained algorithm has the ability to automatically adjust the search direction according to the feedback from experiments. Under some mild assumptions, we use the generalized line search with non-monotonicity to obtain remarkable results, which not only establishes the global convergence of the algorithm for general functions, but also R-linear convergence for uniformly convex functions is further proved. The numerical performance for both the traditional test functions and image restoration problems show that the proposed algorithm is efficient.

scholarly journals A Modified Nonlinear Conjugate Gradient Method with the Armijo Line Search and Its Application

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Mengxiang Zhang ◽  
Yingjie Zhou ◽  
Songhua Wang
Keyword(s):  
Image Restoration ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Line Search ◽  
Gradient Methods ◽  
Linear Convergence ◽  
Nonlinear Conjugate Gradient Method ◽  
Armijo Line Search ◽  
Nonlinear Conjugate Gradient

In this article, a modified Polak-Ribière-Polyak (PRP) conjugate gradient method is proposed for image restoration. The presented method can generate sufficient descent directions without any line search conditions. Under some mild conditions, this method is globally convergent with the Armijo line search. Moreover, the linear convergence rate of the modified PRP method is established. The experimental results of unconstrained optimization, image restoration, and compressive sensing show that the proposed method is promising and competitive with other conjugate gradient methods.

scholarly journals Energetic-Property-Preserving Numerical Schemes for Coupled Natural Systems

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 249
Author(s):  
Mizuka Komatsu ◽  
Shunpei Terakawa ◽  
Takaharu Yaguchi
Keyword(s):  
Gradient Method ◽  
Symmetric Matrix ◽  
Coupled Systems ◽  
Numerical Schemes ◽  
Natural Systems ◽  
Discrete Gradient ◽  
Discrete Gradient Method ◽  
Spring System ◽  
Mass Spring ◽  
Energetic Property

In this paper, we propose a method for deriving energetic-property-preserving numerical schemes for coupled systems of two given natural systems. We consider the case where the two systems are interconnected by the action–reaction law. Although the derived schemes are based on the discrete gradient method, in the case under consideration, the equation of motion is not of the usual form represented by using the skew-symmetric matrix. Hence, the energetic-property-preserving schemes cannot be obtained by straightforwardly using the discrete gradient method. We show numerical results for two coupled systems as examples; the first system is a combination of the wave equation and the elastic equation, and the second is of the mass–spring system and the elastic equation.

A Method for Computation of Wave Propagation in Heterogeneous Solids: Implementation and Performance

2013 ◽  
Author(s):  
S. S. Cho ◽  
K. C. Park ◽  
R. Kolman
Keyword(s):  
Wave Propagation ◽  
Plane Stress ◽  
Three Dimensional ◽  
High Fidelity ◽  
Computer Implementation ◽  
Heterogeneous Solids ◽  
Computational Performance ◽  
Numerical Performance ◽  
And Performance ◽  
Present Algorithm

Computer implementation of the new algorithm developed in [1, 2, 3] and its numerical performance is presented, with detailed discussions of the element-by-element decomposition of the extensional and shear components and step-by-step algorithmic procedures. Numerical results as applied to wave propagating through cracked plane stress problems, three-dimensional problems and elasto-plastic problems illustrate high-fidelity of the present algorithm compared with existing ones, and the new algorithm is implemented into an open source research code TAHOE[4] code along with the further computational performance.

Higher-Order Plate Elements for Large Deformation Analysis in Multibody Applications

2016 ◽  
Author(s):  
Henrik Ebel ◽  
Marko K. Matikainen ◽  
Vesa-Ville Hurskainen ◽  
Aki Mikkola
Keyword(s):  
Large Deformation ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Higher Order ◽  
Deformation Analysis ◽  
Numerical Convergence ◽  
Plate Elements ◽  
Negative Effect ◽  
Numerical Performance ◽  
Locking Phenomena

This study introduces higher-order three-dimensional plate elements based on the absolute nodal coordinate formulation (ANCF) for large deformation multibody applications. The introduced elements employ four to eight nodes and the St. Venant-Kirchhoff material law. A newly proposed eight-node element is carefully verified using various numerical experiments intended to discover possible locking phenomena. In the introduced plate elements, the usage of polynomial approximations of second order in all three directions is found to be advantageous in terms of numerical performance. A comparison of the proposed eight-node element to the introduced four-node higher-order plate elements reveals that the usage of in-plane slopes as nodal degrees of freedom has a negative effect on numerical convergence properties in thin-plate use-cases.

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