Approximating of functions from holder classes Hα [0, 1] by haar wavelets
In the present work, a new direct computational method for solving definite integrals based on Haar wavelets is introduced. The definite integral of the functions from Holder classes is replaced with the approximation of the function by Haar wavelets and the the calculation of definite integrals is...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Institute of Physics Publishing
2017
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| Online Access: | http://psasir.upm.edu.my/id/eprint/60919/1/Approximating%20of%20functions%20from%20holder%20classes%20H%CE%B1%20%5B0%2C%201%5D%20by%20haar%20wavelets.pdf |
| _version_ | 1796977383192920064 |
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| author | Ahatjonovich, Anvarjon Ahmedov Abdul Sathar, Mohammad Hasan Rasedee, Ahmad Fadly Nurullah Mohd Mokhtar, Nor Fadzilah |
| author_facet | Ahatjonovich, Anvarjon Ahmedov Abdul Sathar, Mohammad Hasan Rasedee, Ahmad Fadly Nurullah Mohd Mokhtar, Nor Fadzilah |
| author_sort | Ahatjonovich, Anvarjon Ahmedov |
| collection | UPM |
| description | In the present work, a new direct computational method for solving definite integrals based on Haar wavelets is introduced. The definite integral of the functions from Holder classes is replaced with the approximation of the function by Haar wavelets and the the calculation of definite integrals is reduced to the problem of solving algebraic equation formed by the Fourier coefficients in terms of Haar wavelets. Based on the properties of the Haar wavelets it is shown that the such approximations much better approximate the value of the integrals for the functions from Holder classes. The Error analysis of the approximation method are worked out in the classes of Holder to show the efficiency of the new method and connection of the module of difference with smoothness of the function is established. Finally, some numerical examples of the implementation the method for the functions from Holder classes are presented. |
| first_indexed | 2024-03-06T09:39:15Z |
| format | Article |
| id | upm.eprints-60919 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T09:39:15Z |
| publishDate | 2017 |
| publisher | Institute of Physics Publishing |
| record_format | dspace |
| spelling | upm.eprints-609192019-03-21T08:10:03Z http://psasir.upm.edu.my/id/eprint/60919/ Approximating of functions from holder classes Hα [0, 1] by haar wavelets Ahatjonovich, Anvarjon Ahmedov Abdul Sathar, Mohammad Hasan Rasedee, Ahmad Fadly Nurullah Mohd Mokhtar, Nor Fadzilah In the present work, a new direct computational method for solving definite integrals based on Haar wavelets is introduced. The definite integral of the functions from Holder classes is replaced with the approximation of the function by Haar wavelets and the the calculation of definite integrals is reduced to the problem of solving algebraic equation formed by the Fourier coefficients in terms of Haar wavelets. Based on the properties of the Haar wavelets it is shown that the such approximations much better approximate the value of the integrals for the functions from Holder classes. The Error analysis of the approximation method are worked out in the classes of Holder to show the efficiency of the new method and connection of the module of difference with smoothness of the function is established. Finally, some numerical examples of the implementation the method for the functions from Holder classes are presented. Institute of Physics Publishing 2017 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/60919/1/Approximating%20of%20functions%20from%20holder%20classes%20H%CE%B1%20%5B0%2C%201%5D%20by%20haar%20wavelets.pdf Ahatjonovich, Anvarjon Ahmedov and Abdul Sathar, Mohammad Hasan and Rasedee, Ahmad Fadly Nurullah and Mohd Mokhtar, Nor Fadzilah (2017) Approximating of functions from holder classes Hα [0, 1] by haar wavelets. Journal of Physics: Conference Series, 890. pp. 1-7. ISSN 1742-6588; ESSN: 1742-6596 https://iopscience.iop.org/article/10.1088/1742-6596/890/1/012073/pdf 10.1088/1742-6596/890/1/012073 |
| spellingShingle | Ahatjonovich, Anvarjon Ahmedov Abdul Sathar, Mohammad Hasan Rasedee, Ahmad Fadly Nurullah Mohd Mokhtar, Nor Fadzilah Approximating of functions from holder classes Hα [0, 1] by haar wavelets |
| title | Approximating of functions from holder classes Hα [0, 1] by haar wavelets |
| title_full | Approximating of functions from holder classes Hα [0, 1] by haar wavelets |
| title_fullStr | Approximating of functions from holder classes Hα [0, 1] by haar wavelets |
| title_full_unstemmed | Approximating of functions from holder classes Hα [0, 1] by haar wavelets |
| title_short | Approximating of functions from holder classes Hα [0, 1] by haar wavelets |
| title_sort | approximating of functions from holder classes hα 0 1 by haar wavelets |
| url | http://psasir.upm.edu.my/id/eprint/60919/1/Approximating%20of%20functions%20from%20holder%20classes%20H%CE%B1%20%5B0%2C%201%5D%20by%20haar%20wavelets.pdf |
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