Smoothness for Some Selected Test Functions Relative to Shape Parameter via IMQ

α
K. Issa
K. Issa
σ
B. O. Sanni
B. O. Sanni
α Kwara State University Kwara State University

Send Message

To: Author

Smoothness for Some Selected Test Functions Relative to Shape Parameter via IMQ

Article Fingerprint

ReserarchID

XWM4K

Smoothness for Some Selected Test Functions Relative to Shape Parameter via IMQ Banner

AI TAKEAWAY

Connecting with the Eternal Ground
  • English
  • Afrikaans
  • Albanian
  • Amharic
  • Arabic
  • Armenian
  • Azerbaijani
  • Basque
  • Belarusian
  • Bengali
  • Bosnian
  • Bulgarian
  • Catalan
  • Cebuano
  • Chichewa
  • Chinese (Simplified)
  • Chinese (Traditional)
  • Corsican
  • Croatian
  • Czech
  • Danish
  • Dutch
  • Esperanto
  • Estonian
  • Filipino
  • Finnish
  • French
  • Frisian
  • Galician
  • Georgian
  • German
  • Greek
  • Gujarati
  • Haitian Creole
  • Hausa
  • Hawaiian
  • Hebrew
  • Hindi
  • Hmong
  • Hungarian
  • Icelandic
  • Igbo
  • Indonesian
  • Irish
  • Italian
  • Japanese
  • Javanese
  • Kannada
  • Kazakh
  • Khmer
  • Korean
  • Kurdish (Kurmanji)
  • Kyrgyz
  • Lao
  • Latin
  • Latvian
  • Lithuanian
  • Luxembourgish
  • Macedonian
  • Malagasy
  • Malay
  • Malayalam
  • Maltese
  • Maori
  • Marathi
  • Mongolian
  • Myanmar (Burmese)
  • Nepali
  • Norwegian
  • Pashto
  • Persian
  • Polish
  • Portuguese
  • Punjabi
  • Romanian
  • Russian
  • Samoan
  • Scots Gaelic
  • Serbian
  • Sesotho
  • Shona
  • Sindhi
  • Sinhala
  • Slovak
  • Slovenian
  • Somali
  • Spanish
  • Sundanese
  • Swahili
  • Swedish
  • Tajik
  • Tamil
  • Telugu
  • Thai
  • Turkish
  • Ukrainian
  • Urdu
  • Uzbek
  • Vietnamese
  • Welsh
  • Xhosa
  • Yiddish
  • Yoruba
  • Zulu

Abstract

Radial basis function (RBF) approximation has the potential to provide accurate function approximations for large data site given at scattered node locations which yields smooth solutions for a given number of node points especially when the basis functions are scaled to be nearly at and when the shape parameter is choose wisely. In this paper, we concentrate on the choice of shape parameter, which must be choose wisely and the simplest strategy we adopt is to perform a series of interpolation experiments by varying the interval of shape parameter, and then pick the best” one. The best” was pick by checking the errors for different data sites and the smoothness of the error graphs. The results shows that the choice of interval for the shape parameter give better accuracy and smoothness of the graphs.

References

24 Cites in Article
  1. J Biazar,M Hosami Selection of an interval for variable shape parameter in approximation by radial basis funtions.
  2. J Biazar,M Hosami Selection of an interval for variable shape parameter in approximation by radial basis funtions.
  3. Mehdi Dehghan,Ali Shokri (2009). Numerical solution of the nonlinear Klein–Gordon equation using radial basis functions.
  4. J Wertz,E Kansa,L Ling (2006). The role of the multiquadric shape parameters in solving elliptic partial differential equations.
  5. Ulrika Pettersson,Elisabeth Larsson,Gunnar Marcusson,Jonas Persson (2008). Improved radial basis function methods for multi-dimensional option pricing.
  6. Mira Bozzini,Licia Lenarduzzi,Robert Schaback (2002). Adaptive Interpolation by Scaled Multiquadrics.
  7. H Wendland (2005). Scattered data approximation.
  8. S Deparis,D Forti,A Quarteroni (2014). A rescaled localized radial basis function interpolation on non-cartesian and nonconforming grids.
  9. E Larsson,E Lehto,A Heryudono,B Fornberg (2013). Stable computation of differentiation matrices and scattered node stencils based on Gaussian radial basis functions.
  10. M Buhmann (2003). Radial Basis Functions: Theory and Implementations.
  11. Gregory Fasshauer (2007). Meshfree Approximation Methods with Matlab.
  12. Armin Iske (2002). Scattered Data Modelling Using Radial Basis Functions.
  13. G Fasshauer (1997). Solving partial di_erential equations by collocation with radial basis functions in Surface Fitting and Multire solution Methods.
  14. A Fedoseyev,M Friedman,E Kansa (2002). Improved multiquadric method for elliptic partial differential equations via PDE collocation on the boundary.
  15. S Sarra,E Kansa (2009). Multiquadric Radial Basis Function Approximation Methods for the Numerical Solution of Partial Differential Equations.
  16. Mehdi Tatari,Mehdi Dehghan (2009). On the solution of the non-local parabolic partial differential equations via radial basis functions.
  17. E Kansa,R Carlson (1992). Improved accuracy of multiquadric interpolation using variable shape parameters.
  18. B Fornberg,G Wright (2004). Stable computation of multiquadric interpolants for all values of the shape parameter.
  19. M Bozzini,L Lenarduzzi,R Schaback (2002). Adaptive interpolation by scaled multiquadrics.
  20. E Kansa,R Carlson (1992). Improved accuracy of multiquadric interpolation using variable shape parameters.
  21. Bengt Fornberg,Julia Zuev (2007). The Runge phenomenon and spatially variable shape parameters in RBF interpolation.
  22. Robert Schaback,Holger Wendland (2000). Adaptive greedy techniques for approximate solution of large RBF systems.
  23. Song Xiang,Ke-Ming Wang,Yan-Ting Ai,Yun-Dong Sha,Hong Shi (2012). Trigonometric variable shape parameter and exponent strategy for generalized multiquadric radial basis function approximation.
  24. S Sarra,D Sturgill (2009). A random variable shape parameter strategy for radial basis function approximation methods.

Funding

No external funding was declared for this work.

Conflict of Interest

The authors declare no conflict of interest.

Ethical Approval

No ethics committee approval was required for this article type.

Data Availability

Not applicable for this article.

How to Cite This Article

K. Issa. 2017. \u201cSmoothness for Some Selected Test Functions Relative to Shape Parameter via IMQ\u201d. Global Journal of Science Frontier Research - F: Mathematics & Decision GJSFR-F Volume 17 (GJSFR Volume 17 Issue F2): .

Download Citation

Issue Cover
GJSFR Volume 17 Issue F2
Pg. 29- 36
Journal Specifications

Crossref Journal DOI 10.17406/GJSFR

Print ISSN 0975-5896

e-ISSN 2249-4626

Keywords
Classification
GJSFR-F Classification: 65L99
Version of record

v1.2

Issue date

March 24, 2017

Language
en
Experiance in AR

Explore published articles in an immersive Augmented Reality environment. Our platform converts research papers into interactive 3D books, allowing readers to view and interact with content using AR and VR compatible devices.

Read in 3D

Your published article is automatically converted into a realistic 3D book. Flip through pages and read research papers in a more engaging and interactive format.

Article Matrices
Total Views: 3526
Total Downloads: 1740
2026 Trends
Related Research

Published Article

Radial basis function (RBF) approximation has the potential to provide accurate function approximations for large data site given at scattered node locations which yields smooth solutions for a given number of node points especially when the basis functions are scaled to be nearly at and when the shape parameter is choose wisely. In this paper, we concentrate on the choice of shape parameter, which must be choose wisely and the simplest strategy we adopt is to perform a series of interpolation experiments by varying the interval of shape parameter, and then pick the best” one. The best” was pick by checking the errors for different data sites and the smoothness of the error graphs. The results shows that the choice of interval for the shape parameter give better accuracy and smoothness of the graphs.

Our website is actively being updated, and changes may occur frequently. Please clear your browser cache if needed. For feedback or error reporting, please email [email protected]

Request Access

Please fill out the form below to request access to this research paper. Your request will be reviewed by the editorial or author team.
X

Quote and Order Details

Contact Person

Invoice Address

Notes or Comments

This is the heading

Lorem ipsum dolor sit amet, consectetur adipiscing elit. Ut elit tellus, luctus nec ullamcorper mattis, pulvinar dapibus leo.

High-quality academic research articles on global topics and journals.

Smoothness for Some Selected Test Functions Relative to Shape Parameter via IMQ

K. Issa
K. Issa Kwara State University
B. O. Sanni
B. O. Sanni

Research Journals