Almost Optimality of the Orthogonal Super Greedy Algorithm for <i>μ</i>-Coherent Dictionaries
We study the approximation capability of the orthogonal super greedy algorithm (OSGA) with respect to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>μ</mi></semantics></math></inline-fo...
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MDPI AG
2022-04-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/11/5/186 |
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| author | Chunfang Shao Jincai Chang Peixin Ye Wenhui Zhang Shuo Xing |
| author_facet | Chunfang Shao Jincai Chang Peixin Ye Wenhui Zhang Shuo Xing |
| author_sort | Chunfang Shao |
| collection | DOAJ |
| description | We study the approximation capability of the orthogonal super greedy algorithm (OSGA) with respect to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>μ</mi></semantics></math></inline-formula>-coherent dictionaries in Hilbert spaces. We establish the Lebesgue-type inequalities for OSGA, which show that the OSGA provides an almost optimal approximation on the first <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>[</mo><mn>1</mn><mo>/</mo><mo stretchy="false">(</mo><mn>18</mn><mspace width="3.33333pt"></mspace><mi mathvariant="sans-serif">μ</mi><mi mathvariant="normal">s</mi><mo>)</mo><mo>]</mo></mrow></semantics></math></inline-formula> steps. Moreover, we improve the asymptotic constant in the Lebesgue-type inequality of OGA obtained by Livshitz E D. |
| first_indexed | 2024-03-10T03:20:39Z |
| format | Article |
| id | doaj.art-a6db6651ef144d8299406c7301bca30e |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-10T03:20:39Z |
| publishDate | 2022-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-a6db6651ef144d8299406c7301bca30e2023-11-23T10:03:47ZengMDPI AGAxioms2075-16802022-04-0111518610.3390/axioms11050186Almost Optimality of the Orthogonal Super Greedy Algorithm for <i>μ</i>-Coherent DictionariesChunfang Shao0Jincai Chang1Peixin Ye2Wenhui Zhang3Shuo Xing4College of Science, North China University of Science and Technology, Tangshan 063210, ChinaCollege of Science, North China University of Science and Technology, Tangshan 063210, ChinaSchool of Mathematics and LPMC, Nankai University, Tianjin 300071, ChinaSchool of Mathematics and LPMC, Nankai University, Tianjin 300071, ChinaSchool of Mathematics and LPMC, Nankai University, Tianjin 300071, ChinaWe study the approximation capability of the orthogonal super greedy algorithm (OSGA) with respect to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>μ</mi></semantics></math></inline-formula>-coherent dictionaries in Hilbert spaces. We establish the Lebesgue-type inequalities for OSGA, which show that the OSGA provides an almost optimal approximation on the first <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>[</mo><mn>1</mn><mo>/</mo><mo stretchy="false">(</mo><mn>18</mn><mspace width="3.33333pt"></mspace><mi mathvariant="sans-serif">μ</mi><mi mathvariant="normal">s</mi><mo>)</mo><mo>]</mo></mrow></semantics></math></inline-formula> steps. Moreover, we improve the asymptotic constant in the Lebesgue-type inequality of OGA obtained by Livshitz E D.https://www.mdpi.com/2075-1680/11/5/186orthogonal super greedy algorighmcoherencebest <i>n</i>-term approximationLebesgue-type inequality |
| spellingShingle | Chunfang Shao Jincai Chang Peixin Ye Wenhui Zhang Shuo Xing Almost Optimality of the Orthogonal Super Greedy Algorithm for <i>μ</i>-Coherent Dictionaries Axioms orthogonal super greedy algorighm coherence best <i>n</i>-term approximation Lebesgue-type inequality |
| title | Almost Optimality of the Orthogonal Super Greedy Algorithm for <i>μ</i>-Coherent Dictionaries |
| title_full | Almost Optimality of the Orthogonal Super Greedy Algorithm for <i>μ</i>-Coherent Dictionaries |
| title_fullStr | Almost Optimality of the Orthogonal Super Greedy Algorithm for <i>μ</i>-Coherent Dictionaries |
| title_full_unstemmed | Almost Optimality of the Orthogonal Super Greedy Algorithm for <i>μ</i>-Coherent Dictionaries |
| title_short | Almost Optimality of the Orthogonal Super Greedy Algorithm for <i>μ</i>-Coherent Dictionaries |
| title_sort | almost optimality of the orthogonal super greedy algorithm for i μ i coherent dictionaries |
| topic | orthogonal super greedy algorighm coherence best <i>n</i>-term approximation Lebesgue-type inequality |
| url | https://www.mdpi.com/2075-1680/11/5/186 |
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