caa a22 4500 605469148 CHVBK 20210128100320.0 cr unu---uuuuu 210128e20150701xx s 000 0 eng 10.1007/s00500-014-1379-5 doi (NATIONALLICENCE)springer-10.1007/s00500-014-1379-5 Mo Yan Department of Mathematics, Faculty of Science and Technology, University of Macau, Taipa, Macau, China aut Applications of SVR to the Aveiro discretization method [Elektronische Daten] [Yan Mo] In Castro et al. (Mathematics without boundaries: surveys in pure mathematics. Springer, New York, 2014), authors proposed a method, called Aveiro discretization method, in their paper to determine whether a given function belongs to a certain reproducing kernel Hilbert space or not, depending on finite data of the given function. The method is effective for many cases where the data are noise free. However, it will loose efficacy if the data are noise corrupted. To deal with noise-corrupted data case, we combine two support vector regression (SVR) algorithms and Averio discretization method, respectively, to determine a given function whether belongs to a certain reproducing kernel Hilbert space. In the text, our approach is phrased as the SVR-based Aveiro discretization method which includes two algorithms, the SVR-Aveiro discretization algorithm and LS-SVR-Aveiro discretization algorithm. The proposed approach is compared with Aveiro discretization method and Linear-SVR-Aveiro discretization algorithm which is combined of linear-SVR and Aveiro discretization method; our approach shows promising results. Springer-Verlag Berlin Heidelberg, 2014 Support vector regression nationallicence Least square support vector regression nationallicence Smooth functions nationallicence Reproducing kernel Hilbert space nationallicence Sobolev space nationallicence Soft Computing Springer Berlin Heidelberg 19/7(2015-07-01), 1939-1951 1432-7643 19:7<1939 2015 19 500 https://doi.org/10.1007/s00500-014-1379-5 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00500-014-1379-5 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Mo Yan Department of Mathematics, Faculty of Science and Technology, University of Macau, Taipa, Macau, China aut NATIONALLICENCE 773 0- Soft Computing Springer Berlin Heidelberg 19/7(2015-07-01), 1939-1951 1432-7643 19:7<1939 2015 19 500