Cheng, Raymond; Wang, Rui; Xu, Yuesheng A duality approach to regularized learning problems in Banach spaces. (English) Zbl 07805473 J. Complexity 81, Article ID 101818, 22 p. (2024). MSC: 68Q32 41A05 46B45 PDFBibTeX XMLCite \textit{R. Cheng} et al., J. Complexity 81, Article ID 101818, 22 p. (2024; Zbl 07805473) Full Text: DOI arXiv
Xu, Yuesheng Sparse machine learning in Banach spaces. (English) Zbl 07705768 Appl. Numer. Math. 187, 138-157 (2023). MSC: 68Txx 46Exx 41Axx PDFBibTeX XMLCite \textit{Y. Xu}, Appl. Numer. Math. 187, 138--157 (2023; Zbl 07705768) Full Text: DOI
Liu, Qianru; Wang, Rui; Xu, Yuesheng; Yan, Mingsong Parameter choices for sparse regularization with the \(\ell_1\) norm. (English) Zbl 07640701 Inverse Probl. 39, No. 2, Article ID 025004, 34 p. (2023). MSC: 47A52 PDFBibTeX XMLCite \textit{Q. Liu} et al., Inverse Probl. 39, No. 2, Article ID 025004, 34 p. (2023; Zbl 07640701) Full Text: DOI arXiv
Wang, Rui; Xu, Yuesheng Representer theorems in Banach spaces: minimum norm interpolation, regularized learning and semi-discrete inverse problems. (English) Zbl 1507.68261 J. Mach. Learn. Res. 22, Paper No. 225, 65 p. (2021). MSC: 68T05 41A65 46B20 46N10 PDFBibTeX XMLCite \textit{R. Wang} and \textit{Y. Xu}, J. Mach. Learn. Res. 22, Paper No. 225, 65 p. (2021; Zbl 1507.68261) Full Text: arXiv Link
Wang, Rui; Xu, Yuesheng Regularization in a functional reproducing kernel Hilbert space. (English) Zbl 07390177 J. Complexity 66, Article ID 101567, 23 p. (2021). MSC: 47-XX PDFBibTeX XMLCite \textit{R. Wang} and \textit{Y. Xu}, J. Complexity 66, Article ID 101567, 23 p. (2021; Zbl 07390177) Full Text: DOI
Guan, Wenchao; Jiang, Ying; Xu, Yuesheng Computing the Newton potential in the boundary integral equation for the Dirichlet problem of the Poisson equation. (English) Zbl 1456.35094 J. Integral Equations Appl. 32, No. 3, 293-324 (2020). MSC: 35J05 65N30 PDFBibTeX XMLCite \textit{W. Guan} et al., J. Integral Equations Appl. 32, No. 3, 293--324 (2020; Zbl 1456.35094) Full Text: DOI Euclid Link
Li, Zheng; Song, Guohui; Xu, Yuesheng A two-step fixed-point proximity algorithm for a class of non-differentiable optimization models in machine learning. (English) Zbl 1423.68382 J. Sci. Comput. 81, No. 2, 923-940 (2019). MSC: 68T05 PDFBibTeX XMLCite \textit{Z. Li} et al., J. Sci. Comput. 81, No. 2, 923--940 (2019; Zbl 1423.68382) Full Text: DOI
Xu, Yuesheng; Ye, Qi Generalized Mercer kernels and reproducing kernel Banach spaces. (English) Zbl 1455.68009 Memoirs of the American Mathematical Society 1243. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-3550-9/pbk; 978-1-4704-5077-9/ebook). vi, 122 p. (2019). Reviewer: Martin D. Buhmann (Gießen) MSC: 68-02 46-02 65-02 46E22 65Dxx 68T05 PDFBibTeX XMLCite \textit{Y. Xu} and \textit{Q. Ye}, Generalized Mercer kernels and reproducing kernel Banach spaces. Providence, RI: American Mathematical Society (AMS) (2019; Zbl 1455.68009) Full Text: DOI arXiv
Wang, Rui; Xu, Yuesheng Functional reproducing kernel Hilbert spaces for non-point-evaluation functional data. (English) Zbl 1423.46046 Appl. Comput. Harmon. Anal. 46, No. 3, 569-623 (2019). MSC: 46E22 68T05 94A20 PDFBibTeX XMLCite \textit{R. Wang} and \textit{Y. Xu}, Appl. Comput. Harmon. Anal. 46, No. 3, 569--623 (2019; Zbl 1423.46046) Full Text: DOI
Jiang, Ying; Wang, Bo; Xu, Yuesheng A fully discrete fast Fourier-Galerkin method solving a boundary integral equation for the biharmonic equation. (English) Zbl 1401.31011 J. Sci. Comput. 76, No. 3, 1594-1632 (2018). MSC: 31A30 31A25 65N30 PDFBibTeX XMLCite \textit{Y. Jiang} et al., J. Sci. Comput. 76, No. 3, 1594--1632 (2018; Zbl 1401.31011) Full Text: DOI
Cao, Yanzhao; Jiang, Ying; Xu, Yuesheng A fast discrete spectral method for stochastic partial differential equations. (English) Zbl 1386.60213 Adv. Comput. Math. 43, No. 5, 973-998 (2017). MSC: 60H15 41A63 78M22 PDFBibTeX XMLCite \textit{Y. Cao} et al., Adv. Comput. Math. 43, No. 5, 973--998 (2017; Zbl 1386.60213) Full Text: DOI
Cao, Yanzhao; Jiang, Ying; Xu, Yuesheng Orthogonal polynomial expansions on sparse grids. (English) Zbl 1300.65009 J. Complexity 30, No. 6, 683-715 (2014). MSC: 65D15 33C45 65T50 26E05 65N35 PDFBibTeX XMLCite \textit{Y. Cao} et al., J. Complexity 30, No. 6, 683--715 (2014; Zbl 1300.65009) Full Text: DOI
Jiang, Ying; Xu, Yuesheng Fast computation of the multidimensional discrete Fourier transform and discrete backward Fourier transform on sparse grids. (English) Zbl 1312.65233 Math. Comput. 83, No. 289, 2347-2384 (2014). Reviewer: S. F. Lukomskii (Saratov) MSC: 65T50 PDFBibTeX XMLCite \textit{Y. Jiang} and \textit{Y. Xu}, Math. Comput. 83, No. 289, 2347--2384 (2014; Zbl 1312.65233) Full Text: DOI
Chen, Xiangling; Wang, Rui; Xu, Yuesheng Fast Fourier-Galerkin methods for nonlinear boundary integral equations. (English) Zbl 1278.65187 J. Sci. Comput. 56, No. 3, 494-514 (2013). Reviewer: Temur Jangveladze (Tbilisi) MSC: 65N38 35J65 65N12 PDFBibTeX XMLCite \textit{X. Chen} et al., J. Sci. Comput. 56, No. 3, 494--514 (2013; Zbl 1278.65187) Full Text: DOI
Liu, Jianqiang; Micchelli, Charles A.; Wang, Rui; Xu, Yuesheng Finite rank kernels for multi-task learning. (English) Zbl 1267.41003 Adv. Comput. Math. 38, No. 2, 427-439 (2013). MSC: 41A05 41A10 46E22 PDFBibTeX XMLCite \textit{J. Liu} et al., Adv. Comput. Math. 38, No. 2, 427--439 (2013; Zbl 1267.41003) Full Text: DOI
Jiang, Ying; Xu, Yuesheng B-spline quasi-interpolation on sparse grids. (English) Zbl 1221.65034 J. Complexity 27, No. 5, 466-488 (2011). Reviewer: Martin D. Buhmann (Gießen) MSC: 65D05 65D07 65D10 PDFBibTeX XMLCite \textit{Y. Jiang} and \textit{Y. Xu}, J. Complexity 27, No. 5, 466--488 (2011; Zbl 1221.65034) Full Text: DOI
Song, Guohui; Xu, Yuesheng Approximation of high-dimensional kernel matrices by multilevel circulant matrices. (English) Zbl 1197.65045 J. Complexity 26, No. 4, 375-405 (2010). Reviewer: Rémi Vaillancourt (Ottawa) MSC: 65F30 65T50 15A09 PDFBibTeX XMLCite \textit{G. Song} and \textit{Y. Xu}, J. Complexity 26, No. 4, 375--405 (2010; Zbl 1197.65045) Full Text: DOI
Jiang, Ying; Xu, Yuesheng Fast Fourier-Galerkin methods for solving singular boundary integral equations: Numerical integration and precondition. (English) Zbl 1193.65206 J. Comput. Appl. Math. 234, No. 9, 2792-2807 (2010). Reviewer: Wilhelm Heinrichs (Essen) MSC: 65N38 65N30 65N12 65F08 35J25 PDFBibTeX XMLCite \textit{Y. Jiang} and \textit{Y. Xu}, J. Comput. Appl. Math. 234, No. 9, 2792--2807 (2010; Zbl 1193.65206) Full Text: DOI
Wang, Bo; Wang, Rui; Xu, Yuesheng Fast Fourier-Galerkin methods for first-kind logarithmic-kernel integral equations on open arcs. (English) Zbl 1193.65232 Sci. China, Math. 53, No. 1, 1-22 (2010). Reviewer: Johannes Elschner (Berlin) MSC: 65R20 45E10 35J05 65N38 65F08 65Y20 PDFBibTeX XMLCite \textit{B. Wang} et al., Sci. China, Math. 53, No. 1, 1--22 (2010; Zbl 1193.65232) Full Text: DOI
Jiang, Ying; Xu, Yuesheng Fast discrete algorithms for sparse Fourier expansions of high dimensional functions. (English) Zbl 1184.65124 J. Complexity 26, No. 1, 51-81 (2010). Reviewer: Manfred Tasche (Rostock) MSC: 65T40 42B05 PDFBibTeX XMLCite \textit{Y. Jiang} and \textit{Y. Xu}, J. Complexity 26, No. 1, 51--81 (2010; Zbl 1184.65124) Full Text: DOI