A least square point of view to reproducing kernel methods to solve functional equations
In this paper we discuss and present a least square and a QR point of view to reproducing kernel methods to approximate solutions to some linear and nonlinear functional equations. The procedure we discuss here may includes ordinary, partial differential, and integral equations. We also give new pro...
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| Published in | Applied mathematics and computation Vol. 357; pp. 206 - 221 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Inc
15.09.2019
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| Abstract | In this paper we discuss and present a least square and a QR point of view to reproducing kernel methods to approximate solutions to some linear and nonlinear functional equations. The procedure we discuss here may includes ordinary, partial differential, and integral equations. We also give new proofs to some known results on this subject. The most interesting contribution is that the proposed algorithm may work even when we know a reproducing kernel but nothing more about the associated reproducing kernel Hilbert space, including the inner product structure. |
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| AbstractList | In this paper we discuss and present a least square and a QR point of view to reproducing kernel methods to approximate solutions to some linear and nonlinear functional equations. The procedure we discuss here may includes ordinary, partial differential, and integral equations. We also give new proofs to some known results on this subject. The most interesting contribution is that the proposed algorithm may work even when we know a reproducing kernel but nothing more about the associated reproducing kernel Hilbert space, including the inner product structure. |
| Author | Baquião, Maria Caruline Ferreira, José Claudinei |
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| Cites_doi | 10.1016/j.aml.2018.06.035 10.22606/aan.2018.31002 10.1007/s00365-009-9080-0 10.1016/j.cam.2017.05.032 10.1016/j.parco.2014.03.003 10.1007/s11117-016-0414-4 10.1016/j.jmaa.2006.05.011 10.1016/j.cam.2016.06.029 10.1002/mana.201100072 10.1007/s11075-015-9970-0 |
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| Keywords | Reproducing kernel Approximation theory Functional equations Positive definite kernel Numerical methods |
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| References | Ferreira, Ferreira (bib0009) 2018; 3 Vahdati, Fardi, Ghasemi (bib0002) 2018; 328 Assari, Dehghan (bib0004) 2018 Li, Wu (bib0005) 2018; 86 Javan, Abbasbandy, Araghi (bib0013) 2017; 2017 Ferreira, Menegatto (bib0015) 2012; 285 Javadi, Babolian, Moradi (bib0012) 2014; 2014 Wathen, Zhu (bib0006) 2015; 70 Fasshauer (bib0001) 2011 Andrew, Dingle (bib0016) 2014; 40 Zhou, Wu, Zhang, Zhang (bib0018) 2007; 184 Minh (bib0003) 2010; 32 Sakar (bib0011) 2017; 309 Webb (bib0017) 2017 Ferreira, Menegatto (bib0008) 2013 Geng, Cui (bib0010) 2007; 327 Ferreira (bib0014) 2017; 21 Berg, Christensen, Ressel (bib0007) 1984; volume 100 Ferreira (10.1016/j.amc.2019.04.008_bib0009) 2018; 3 Javadi (10.1016/j.amc.2019.04.008_bib0012) 2014; 2014 Javan (10.1016/j.amc.2019.04.008_bib0013) 2017; 2017 Berg (10.1016/j.amc.2019.04.008_sbref0007) 1984; volume 100 Webb (10.1016/j.amc.2019.04.008_sbref0017) 2017 Assari (10.1016/j.amc.2019.04.008_bib0004) 2018 Zhou (10.1016/j.amc.2019.04.008_bib0018) 2007; 184 Andrew (10.1016/j.amc.2019.04.008_bib0016) 2014; 40 Geng (10.1016/j.amc.2019.04.008_bib0010) 2007; 327 Fasshauer (10.1016/j.amc.2019.04.008_sbref0001) 2011 Vahdati (10.1016/j.amc.2019.04.008_bib0002) 2018; 328 Ferreira (10.1016/j.amc.2019.04.008_bib0014) 2017; 21 Minh (10.1016/j.amc.2019.04.008_bib0003) 2010; 32 Wathen (10.1016/j.amc.2019.04.008_bib0006) 2015; 70 Ferreira (10.1016/j.amc.2019.04.008_bib0008) 2013 Sakar (10.1016/j.amc.2019.04.008_bib0011) 2017; 309 Ferreira (10.1016/j.amc.2019.04.008_bib0015) 2012; 285 Li (10.1016/j.amc.2019.04.008_bib0005) 2018; 86 |
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| SubjectTerms | Approximation theory Functional equations Numerical methods Positive definite kernel Reproducing kernel |
| Title | A least square point of view to reproducing kernel methods to solve functional equations |
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