APPROXIMATION OF FUNCTION BY CONVOLUTION
This thesis discusses about approximation of functions by convolution. There are convolutors which are dilations of a kernel and those which are kernels without dilation. We discuss suficient conditions for the convolutors and examples of the convolutors. From existing results, we do not find many k...
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id-itb.:347712019-02-14T15:09:56ZAPPROXIMATION OF FUNCTION BY CONVOLUTION Rahmi Kahar, Eka Matematika Indonesia Theses INSTITUT TEKNOLOGI BANDUNG https://digilib.itb.ac.id/gdl/view/34771 This thesis discusses about approximation of functions by convolution. There are convolutors which are dilations of a kernel and those which are kernels without dilation. We discuss suficient conditions for the convolutors and examples of the convolutors. From existing results, we do not find many kernels without dilation as convolutors. A famous kernel without dilation, known as Landau kernel, which is used in the proof of Weierstrass Approximation theorem, has compact support. In this thesis, we will contruct a new kernel without dilation as a convolutor which has support in RS. We will also give an ilustration about its rate of convergence in approximating functions and examples of its application in image processing text |
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Indonesia Indonesia |
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Matematika |
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Matematika Rahmi Kahar, Eka APPROXIMATION OF FUNCTION BY CONVOLUTION |
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This thesis discusses about approximation of functions by convolution. There are convolutors which are dilations of a kernel and those which are kernels without dilation. We discuss suficient conditions for the convolutors and examples of the convolutors. From existing results, we do not find many kernels without dilation as convolutors. A famous kernel without dilation, known as Landau kernel, which is used in the proof of Weierstrass Approximation theorem, has compact support. In this thesis, we will contruct a new kernel without dilation as a convolutor which has support in RS. We will also give an ilustration about its rate of convergence in approximating functions and examples of its application in image processing |
| format |
Theses |
| author |
Rahmi Kahar, Eka |
| author_facet |
Rahmi Kahar, Eka |
| author_sort |
Rahmi Kahar, Eka |
| title |
APPROXIMATION OF FUNCTION BY CONVOLUTION |
| title_short |
APPROXIMATION OF FUNCTION BY CONVOLUTION |
| title_full |
APPROXIMATION OF FUNCTION BY CONVOLUTION |
| title_fullStr |
APPROXIMATION OF FUNCTION BY CONVOLUTION |
| title_full_unstemmed |
APPROXIMATION OF FUNCTION BY CONVOLUTION |
| title_sort |
approximation of function by convolution |
| url |
https://digilib.itb.ac.id/gdl/view/34771 |
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