Special Issue "Iterative Algorithms for Nonlinear Problems: Convergence and Stability"

A special issue of Algorithms (ISSN 1999-4893).

Deadline for manuscript submissions: 31 July 2020.

Special Issue Editors

Special Issue Information

Dear Colleagues,

Many areas of Science and Technology involve the non-trivial task of solving nonlinear problems. Usually, it is not affordable in a direct way and iterative algorithms play a fundamental role in their approach. This area of research has enjoyed a period of an exponential growth in the last number of years.

This Special Issue is mainly dedicated, but not exclusively, to the design, analysis of convergence and stability of new iterative algorithms for solving nonlinear problems. Moreover, their application to practical problems of Engineering and Basic Sciences are of singular interest. The set of algorithms includes, but is not limited to, methods with and without memory, with derivatives of derivative-free, the real or complex dynamics associated to them and an analysis of their convergence that can be local, semilocal or global.

Prof. Dr. Alicia Cordero
Prof. Dr. Juan R. Torregrosa
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Algorithms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1000 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • nonlinear systems
  • nonlinear matrix equations
  • transcendent equations
  • iterative algorithms
  • convergence
  • efficiency
  • chaotic behavior
  • complex or real dynamics
  • fractional nonlinear analysis

Published Papers (2 papers)

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Research

Open AccessFeature PaperArticle
Local Convergence of an Efficient Multipoint Iterative Method in Banach Space
Algorithms 2020, 13(1), 25; https://doi.org/10.3390/a13010025 - 15 Jan 2020
Abstract
We discuss the local convergence of a derivative-free eighth order method in a Banach space setting. The present study provides the radius of convergence and bounds on errors under the hypothesis based on the first Fréchet-derivative only. The approaches of using Taylor expansions, [...] Read more.
We discuss the local convergence of a derivative-free eighth order method in a Banach space setting. The present study provides the radius of convergence and bounds on errors under the hypothesis based on the first Fréchet-derivative only. The approaches of using Taylor expansions, containing higher order derivatives, do not provide such estimates since the derivatives may be nonexistent or costly to compute. By using only first derivative, the method can be applied to a wider class of functions and hence its applications are expanded. Numerical experiments show that the present results are applicable to the cases wherein previous results cannot be applied. Full article
Open AccessArticle
Image Restoration Using a Fixed-Point Method for a TVL2 Regularization Problem
Algorithms 2020, 13(1), 1; https://doi.org/10.3390/a13010001 - 18 Dec 2019
Abstract
In this paper, we first propose a new TVL2 regularization model for image restoration, and then we propose two iterative methods, which are fixed-point and fixed-point-like methods, using CGLS (Conjugate Gradient Least Squares method) for solving the new proposed TVL2 problem. We also [...] Read more.
In this paper, we first propose a new TVL2 regularization model for image restoration, and then we propose two iterative methods, which are fixed-point and fixed-point-like methods, using CGLS (Conjugate Gradient Least Squares method) for solving the new proposed TVL2 problem. We also provide convergence analysis for the fixed-point method. Lastly, numerical experiments for several test problems are provided to evaluate the effectiveness of the proposed two iterative methods. Numerical results show that the new proposed TVL2 model is preferred over an existing TVL2 model and the proposed fixed-point-like method is well suited for the new TVL2 model. Full article
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