scholarly journals Finding Dantzig selectors with a proximity operator based fixed-point algorithm

2015 ◽  
Vol 90 ◽  
pp. 36-46 ◽  
Author(s):  
Ashley Prater ◽  
Lixin Shen ◽  
Bruce W. Suter
Keyword(s):  
Fixed Point ◽  
Proximity Operator ◽  
Fixed Point Algorithm

An Eccentric Barycentric fixed Point Algorithm

1977 ◽  
Vol 2 (4) ◽  
pp. 343-359 ◽  
Author(s):  
Willard I. Zangwill
Keyword(s):  
Fixed Point ◽  
Fixed Point Algorithm

scholarly journals Numerical Algorithms for Elastoplacity: Finite Elements Code Development and Implementation of the Mohr–Coulomb Law

2021 ◽  
Vol 11 (10) ◽  
pp. 4637
Author(s):  
Gildas Yaovi Amouzou ◽  
Azzeddine Soulaïmani
Keyword(s):  
Fixed Point ◽  
Finite Difference ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Numerical Algorithms ◽  
Constitutive Law ◽  
Layer By Layer ◽  
Implementation Framework ◽  
Fixed Point Algorithm ◽  
Tangent Matrix

Two numerical algorithms for solving elastoplastic problems with the finite element method are presented. The first deals with the implementation of the return mapping algorithm and is based on a fixed-point algorithm. This method rewrites the system of elastoplasticity non-linear equations in a form adapted to the fixed-point method. The second algorithm relates to the computation of the elastoplastic consistent tangent matrix using a simple finite difference scheme. A first validation is performed on a nonlinear bar problem. The results obtained show that both numerical algorithms are very efficient and yield the exact solution. The proposed algorithms are applied to a two-dimensional rockfill dam loaded in plane strain. The elastoplastic tangent matrix is calculated by using the finite difference scheme for Mohr–Coulomb’s constitutive law. The results obtained with the developed algorithms are very close to those obtained via the commercial software PLAXIS. It should be noted that the algorithm’s code, developed under the Matlab environment, offers the possibility of modeling the construction phases (i.e., building layer by layer) by activating the different layers according to the imposed loading. This algorithmic and implementation framework allows to easily integrate other laws of nonlinear behaviors, including the Hardening Soil Model.

FastNMF

2010 ◽  
pp. 137-163
Author(s):  
Le Li ◽  
Le Li ◽  
Yu-Jin Zhang ◽  
Yu-Jin Zhang
Keyword(s):  
Feature Extraction ◽  
Fixed Point ◽  
Dimensionality Reduction ◽  
Matrix Factorization ◽  
Ease Of Use ◽  
Experimental Results ◽  
Fixed Point Algorithm ◽  
Popular Method ◽  
Face Images ◽  
Multiplicative Update

Non-negative matrix factorization (NMF) is a more and more popular method for non-negative dimensionality reduction and feature extraction of non-negative data, especially face images. Currently no NMF algorithm holds not only satisfactory efficiency for dimensionality reduction and feature extraction of face images but also high ease of use. To improve the applicability of NMF, this chapter proposes a new monotonic, fixed-point algorithm called FastNMF by implementing least squares error-based non-negative factorization essentially according to the basic properties of parabola functions. The minimization problem corresponding to an operation in FastNMF can be analytically solved just by this operation, which is far beyond existing NMF algorithms’ power, and therefore FastNMF holds much higher efficiency, which is validated by a set of experimental results. For the simplicity of design philosophy, FastNMF is still one of NMF algorithms that are the easiest to use and the most comprehensible. Besides, theoretical analysis and experimental results also show that FastNMF tends to extract facial features with better representation ability than popular multiplicative update-based algorithms.

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