Fast Analytic Sampling Approximation from Cauchy Kernel
The paper aims at establishing a fast numerical algorithm for Bk(f), where f is any function in the Hardy space H2(Td) and k is the scale level. Here, Bk(f) is an approximation to f we recently constructed by applying the multiscale transform to the Cauchy kernel. We establish the matrix expression...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2016-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2016/5780718 |
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| _version_ | 1832560398547550208 |
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| author | Youfa Li Jing Shang Honglei Yang Gengrong Zhang Shouzhi Yang |
| author_facet | Youfa Li Jing Shang Honglei Yang Gengrong Zhang Shouzhi Yang |
| author_sort | Youfa Li |
| collection | DOAJ |
| description | The paper aims at establishing a fast numerical algorithm for Bk(f), where f is any function in the Hardy space H2(Td) and k is the scale level. Here, Bk(f) is an approximation to f we recently constructed by applying the multiscale transform to the Cauchy kernel. We establish the matrix expression of Bk(f) and find that it has the structure of a multilevel Hankel matrix. Based on the structure, a fast numerical algorithm is established to compute Bk(f). The computational complexity is given. A numerical experiment is carried out to check the efficiency of our algorithm. |
| format | Article |
| id | doaj-art-8113cb65de4f429fa1efd591aa05fd73 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-8113cb65de4f429fa1efd591aa05fd732025-02-03T01:27:45ZengWileyJournal of Function Spaces2314-88962314-88882016-01-01201610.1155/2016/57807185780718Fast Analytic Sampling Approximation from Cauchy KernelYoufa Li0Jing Shang1Honglei Yang2Gengrong Zhang3Shouzhi Yang4College of Mathematics and Information Science, Guangxi University, ChinaCollege of Mathematics and Information Science, Guangxi University, ChinaCollege of Mathematics and Information Science, Guangxi University, ChinaCollege of Mathematics and Information Science, Guangxi University, ChinaDepartment of Mathematics, Shantou University, ChinaThe paper aims at establishing a fast numerical algorithm for Bk(f), where f is any function in the Hardy space H2(Td) and k is the scale level. Here, Bk(f) is an approximation to f we recently constructed by applying the multiscale transform to the Cauchy kernel. We establish the matrix expression of Bk(f) and find that it has the structure of a multilevel Hankel matrix. Based on the structure, a fast numerical algorithm is established to compute Bk(f). The computational complexity is given. A numerical experiment is carried out to check the efficiency of our algorithm.http://dx.doi.org/10.1155/2016/5780718 |
| spellingShingle | Youfa Li Jing Shang Honglei Yang Gengrong Zhang Shouzhi Yang Fast Analytic Sampling Approximation from Cauchy Kernel Journal of Function Spaces |
| title | Fast Analytic Sampling Approximation from Cauchy Kernel |
| title_full | Fast Analytic Sampling Approximation from Cauchy Kernel |
| title_fullStr | Fast Analytic Sampling Approximation from Cauchy Kernel |
| title_full_unstemmed | Fast Analytic Sampling Approximation from Cauchy Kernel |
| title_short | Fast Analytic Sampling Approximation from Cauchy Kernel |
| title_sort | fast analytic sampling approximation from cauchy kernel |
| url | http://dx.doi.org/10.1155/2016/5780718 |
| work_keys_str_mv | AT youfali fastanalyticsamplingapproximationfromcauchykernel AT jingshang fastanalyticsamplingapproximationfromcauchykernel AT hongleiyang fastanalyticsamplingapproximationfromcauchykernel AT gengrongzhang fastanalyticsamplingapproximationfromcauchykernel AT shouzhiyang fastanalyticsamplingapproximationfromcauchykernel |