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Mathematics
Special Issues
Numerical Analysis and Computational Science
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Numerical Analysis and Computational Science

A special issue of Mathematics (ISSN 2227-7390).

Deadline for manuscript submissions: closed (15 November 2021) | Viewed by 5776

Special Issue Editor

Prof. Dr. Anton Iliev

E-Mail Website
Guest Editor
Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 24, Tzar Asen Str., 4000 Plovdiv, Bulgaria
Interests: numerical methods; information systems

Special Issue Information

Nowadays, the need for numerical methods with improved computational characteristics is becoming increasingly important. Special attention deserves to be paid to new and improved theoretical results which lead to ameliorated algorithms with wider applicability and better numerical effectiveness for a number of applied problems in the field of practical computer science. In this regard, especially valuable for modern science are areas of: activation and adaptive functions with applications, smooth approximation, reliability analysis, improved in computational aspects algorithms, etc.

Prof. Dr. Anton Iliev
Guest Editor

Manuscript Submission Information

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Keywords

  • numerical methods
  • activation and adaptive functions with applications
  • smooth approximation
  • reliability analysis
  • improved in computational aspects algorithms

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Published Papers (2 papers)

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Research

17 pages, 9304 KiB  
Article
Approximation of Generalized Ovals and Lemniscates towards Geometric Modeling
by Valery Ochkov, Inna Vasileva, Ekaterina Borovinskaya and Wladimir Reschetilowski
Mathematics 2021, 9(24), 3325; https://doi.org/10.3390/math9243325 - 20 Dec 2021
Cited by 1 | Viewed by 3286
Abstract
This paper considers an approach towards the building of new classes of symmetric closed curves with two or more focal points, which can be obtained by generalizing classical definitions of the ellipse, Cassini, and Cayley ovals. A universal numerical method for creating such [...] Read more.
This paper considers an approach towards the building of new classes of symmetric closed curves with two or more focal points, which can be obtained by generalizing classical definitions of the ellipse, Cassini, and Cayley ovals. A universal numerical method for creating such curves in mathematical packages is introduced. Specific aspects of the provided numerical data in computer-aided design systems with B-splines for three-dimensional modeling are considered. The applicability of the method is demonstrated, as well as the possibility to provide high smoothness of the curvature profile at the specified accuracy of modeling. Full article
(This article belongs to the Special Issue Numerical Analysis and Computational Science)
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15 pages, 581 KiB  
Article
Some Intrinsic Properties of Tadmor–Tanner Functions: Related Problems and Possible Applications
by Nikolay Kyurkchiev
Mathematics 2020, 8(11), 1963; https://doi.org/10.3390/math8111963 - 5 Nov 2020
Cited by 28 | Viewed by 1583
Abstract
In this paper, we study some properties of an exponentially optimal filter proposed by Tadmor and Tanner. More precisely, we consider the problem for approximating the function of rectangular type F(t) by the class of exponential functions [...] Read more.
In this paper, we study some properties of an exponentially optimal filter proposed by Tadmor and Tanner. More precisely, we consider the problem for approximating the function of rectangular type F(t) by the class of exponential functions σadapt(t) about the Hausdorff metric. We prove upper and lower estimates for “saturation”—d (in the case q=2). New activation and “semi-activation” functions based on σadapt(t) are defined. Some related problems are discussed. We also consider modified families of functions with “polynomial variable transfer”. Numerical examples, illustrating our results using CAS MATHEMATICA are given. Full article
(This article belongs to the Special Issue Numerical Analysis and Computational Science)
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