Finding points of importance for radial basis function approximation of large scattered data

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F20%3A43961926" target="_blank" >RIV/49777513:23520/20:43961926 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.springer.com/series/558" target="_blank" >https://www.springer.com/series/558</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/978-3-030-50433-5_19" target="_blank" >10.1007/978-3-030-50433-5_19</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Finding points of importance for radial basis function approximation of large scattered data

Popis výsledku v původním jazyce

Interpolation and approximation methods are used in many fields such as in engineering as well as other disciplines for various scientific discoveries. If the data domain is formed by scattered data, approximation methods may become very complicated as well as time-consuming. Usually, the given data is tessellated by some method, not necessarily the Delaunay triangulation, to produce triangular or tetrahedral meshes. After that approximation methods can be used to produce the surface. However, it is difficult to ensure the continuity and smoothness of the final interpolant along with all adjacent triangles. In this contribution, a meshless approach is proposed by using radial basis functions (RBFs). It is applicable to explicit functions of two variables and it is suitable for all types of scattered data in general. The key point for the RBF approximation is finding the important points that give a good approximation with high precision to the scattered data. Since the compactly supported RBFs (CSRBF) has limited influence in numerical computation, large data sets can be processed efficiently as well as very fast via some efficient algorithm. The main advantage of the RBF is, that it leads to a solution of a system of linear equations (SLE) Ax = b. Thus any efficient method solves the systems of linear equations that can be used. In this study is we propose a new method of determining the importance points on the scattered data that produces a very good reconstructed surface with higher accuracy while maintaining the smoothness of the surface.

Název v anglickém jazyce

Finding points of importance for radial basis function approximation of large scattered data

Popis výsledku anglicky

Interpolation and approximation methods are used in many fields such as in engineering as well as other disciplines for various scientific discoveries. If the data domain is formed by scattered data, approximation methods may become very complicated as well as time-consuming. Usually, the given data is tessellated by some method, not necessarily the Delaunay triangulation, to produce triangular or tetrahedral meshes. After that approximation methods can be used to produce the surface. However, it is difficult to ensure the continuity and smoothness of the final interpolant along with all adjacent triangles. In this contribution, a meshless approach is proposed by using radial basis functions (RBFs). It is applicable to explicit functions of two variables and it is suitable for all types of scattered data in general. The key point for the RBF approximation is finding the important points that give a good approximation with high precision to the scattered data. Since the compactly supported RBFs (CSRBF) has limited influence in numerical computation, large data sets can be processed efficiently as well as very fast via some efficient algorithm. The main advantage of the RBF is, that it leads to a solution of a system of linear equations (SLE) Ax = b. Thus any efficient method solves the systems of linear equations that can be used. In this study is we propose a new method of determining the importance points on the scattered data that produces a very good reconstructed surface with higher accuracy while maintaining the smoothness of the surface.

Druh

D - Stať ve sborníku

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

<a href="/cs/project/GA17-05534S" target="_blank" >GA17-05534S: Meshless metody pro vizualizaci velkých časově-prostorových vektorových dat</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2020

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

ICCS 2020

ISBN

978-3-030-50432-8

ISSN

0302-9743

e-ISSN

1611-3349

Počet stran výsledku

11

Strana od-do

239-250

Název nakladatele

Springer

Místo vydání

Cham

Místo konání akce

Amsterdam, The Netherlands

Datum konání akce

3. 6. 2020

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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