Liu, Guidong; Xiang, Shuhuang An efficient quadrature rule for weakly and strongly singular integrals. (English) Zbl 1511.65155 Appl. Math. Comput. 447, Article ID 127901, 13 p. (2023). MSC: 65R30 35J05 65D32 65T60 PDFBibTeX XMLCite \textit{G. Liu} and \textit{S. Xiang}, Appl. Math. Comput. 447, Article ID 127901, 13 p. (2023; Zbl 1511.65155) Full Text: DOI
Xiang, Shuhuang; Kong, Desong; Liu, Guidong; Wang, Li-Lian Pointwise error estimates and local superconvergence of Jacobi expansions. (English) Zbl 07673302 Math. Comput. 92, No. 342, 1747-1778 (2023). MSC: 65-XX 41A10 41A25 41A50 65N35 65M70 PDFBibTeX XMLCite \textit{S. Xiang} et al., Math. Comput. 92, No. 342, 1747--1778 (2023; Zbl 07673302) Full Text: DOI arXiv
Kong, Desong; Xiang, Shuhuang; Li, Li; Li, Ran Extended barycentric rational schemes for functions of singularities. (English) Zbl 1502.65008 Calcolo 59, No. 4, Paper No. 35, 18 p. (2022). MSC: 65D05 41A20 65D30 PDFBibTeX XMLCite \textit{D. Kong} et al., Calcolo 59, No. 4, Paper No. 35, 18 p. (2022; Zbl 1502.65008) Full Text: DOI
Xiang, Shuhuang Convergence rates on spectral orthogonal projection approximation for functions of algebraic and logarithmatic regularities. (English) Zbl 1465.41003 SIAM J. Numer. Anal. 59, No. 3, 1374-1398 (2021). MSC: 41A10 41A25 41A50 PDFBibTeX XMLCite \textit{S. Xiang}, SIAM J. Numer. Anal. 59, No. 3, 1374--1398 (2021; Zbl 1465.41003) Full Text: DOI arXiv
Kong, Desong; Xiang, Shuhuang Fast linear barycentric rational interpolation for singular functions via scaled transformations. arXiv:2101.07949 Preprint, arXiv:2101.07949 [math.NA] (2021). MSC: 32E30 41A20 41A50 65N35 65M70 BibTeX Cite \textit{D. Kong} and \textit{S. Xiang}, ``Fast linear barycentric rational interpolation for singular functions via scaled transformations'', Preprint, arXiv:2101.07949 [math.NA] (2021) Full Text: arXiv OA License
Xiang, Shuhuang; Liu, Guidong Optimal decay rates on the asymptotics of orthogonal polynomial expansions for functions of limited regularities. (English) Zbl 1511.42024 Numer. Math. 145, No. 1, 117-148 (2020). Reviewer: Alexei Lukashov (Moskva) MSC: 42C05 41A10 41A25 41A50 65N35 65M70 PDFBibTeX XMLCite \textit{S. Xiang} and \textit{G. Liu}, Numer. Math. 145, No. 1, 117--148 (2020; Zbl 1511.42024) Full Text: DOI
Xiang, Shuhuang On the optimal convergence rates of Chebyshev interpolations for functions of limited regularity. (English) Zbl 1471.41008 Appl. Math. Lett. 84, 1-7 (2018). MSC: 41A25 41A10 41A58 PDFBibTeX XMLCite \textit{S. Xiang}, Appl. Math. Lett. 84, 1--7 (2018; Zbl 1471.41008) Full Text: DOI
Xiang, Shuhuang On interpolation approximation: convergence rates for polynomial interpolation for functions of limited regularity. (English) Zbl 1342.65084 SIAM J. Numer. Anal. 54, No. 4, 2081-2113 (2016). MSC: 65D05 41A05 41A10 PDFBibTeX XMLCite \textit{S. Xiang}, SIAM J. Numer. Anal. 54, No. 4, 2081--2113 (2016; Zbl 1342.65084) Full Text: DOI arXiv
Xiang, Shuhuang An improved error bound on Gauss quadrature. (English) Zbl 1336.41012 Appl. Math. Lett. 58, 42-48 (2016). MSC: 41A55 65D30 PDFBibTeX XMLCite \textit{S. Xiang}, Appl. Math. Lett. 58, 42--48 (2016; Zbl 1336.41012) Full Text: DOI
He, Guo; Xiang, Shuhuang; Xu, Zhenhua A Chebyshev collocation method for a class of Fredholm integral equations with highly oscillatory kernels. (English) Zbl 1416.65536 J. Comput. Appl. Math. 300, 354-368 (2016). MSC: 65R20 45B05 PDFBibTeX XMLCite \textit{G. He} et al., J. Comput. Appl. Math. 300, 354--368 (2016; Zbl 1416.65536) Full Text: DOI
Xiang, Shuhuang; Fang, Chunhua; Xu, Zhenhua On uniform approximations to hypersingular finite-part integrals. (English) Zbl 1329.41036 J. Math. Anal. Appl. 435, No. 2, 1210-1228 (2016). MSC: 41A50 65D15 PDFBibTeX XMLCite \textit{S. Xiang} et al., J. Math. Anal. Appl. 435, No. 2, 1210--1228 (2016; Zbl 1329.41036) Full Text: DOI
Xiang, Shuhuang; He, Guo The fast implementation of higher order Hermite-Fejér interpolation. (English) Zbl 1320.65024 SIAM J. Sci. Comput. 37, No. 4, A1727-A1751 (2015). MSC: 65D05 PDFBibTeX XMLCite \textit{S. Xiang} and \textit{G. He}, SIAM J. Sci. Comput. 37, No. 4, A1727--A1751 (2015; Zbl 1320.65024) Full Text: DOI arXiv
Xiang, Shuhuang; He, Guo; Cho, Yeol Je On error bounds of Filon-Clenshaw-Curtis quadrature for highly oscillatory integrals. (English) Zbl 1320.65043 Adv. Comput. Math. 41, No. 3, 573-597 (2015). Reviewer: Denis Sidorov (Irkutsk) MSC: 65D32 41A55 65T40 42A16 PDFBibTeX XMLCite \textit{S. Xiang} et al., Adv. Comput. Math. 41, No. 3, 573--597 (2015; Zbl 1320.65043) Full Text: DOI
He, Guo; Xiang, Shuhuang An improved algorithm for the evaluation of Cauchy principal value integrals of oscillatory functions and its application. (English) Zbl 1305.65107 J. Comput. Appl. Math. 280, 1-13 (2015). MSC: 65D32 65D30 PDFBibTeX XMLCite \textit{G. He} and \textit{S. Xiang}, J. Comput. Appl. Math. 280, 1--13 (2015; Zbl 1305.65107) Full Text: DOI
Xiang, Shuhuang; He, Guo; Wang, Haiyong On fast and stable implementation of Clenshaw-Curtis and Fejér-type quadrature rules. (English) Zbl 1470.65036 Abstr. Appl. Anal. 2014, Article ID 436164, 10 p. (2014). MSC: 65D30 65D32 41A55 PDFBibTeX XMLCite \textit{S. Xiang} et al., Abstr. Appl. Anal. 2014, Article ID 436164, 10 p. (2014; Zbl 1470.65036) Full Text: DOI arXiv
Xu, Zhenhua; Xiang, Shuhuang Numerical evaluation of a class of highly oscillatory integrals involving Airy functions. (English) Zbl 1338.65065 Appl. Math. Comput. 246, 54-63 (2014). MSC: 65D30 33C10 PDFBibTeX XMLCite \textit{Z. Xu} and \textit{S. Xiang}, Appl. Math. Comput. 246, 54--63 (2014; Zbl 1338.65065) Full Text: DOI
Xiang, Shuhuang On convergence rates of Fejér and Gauss-Chebyshev quadrature rules. (English) Zbl 1306.65171 J. Math. Anal. Appl. 405, No. 2, 687-699 (2013). MSC: 65D30 PDFBibTeX XMLCite \textit{S. Xiang}, J. Math. Anal. Appl. 405, No. 2, 687--699 (2013; Zbl 1306.65171) Full Text: DOI
Kang, Hongchao; Xiang, Shuhuang; He, Guo Computation of integrals with oscillatory and singular integrands using Chebyshev expansions. (English) Zbl 1255.65073 J. Comput. Appl. Math. 242, 141-156 (2013). MSC: 65D32 65D30 PDFBibTeX XMLCite \textit{H. Kang} et al., J. Comput. Appl. Math. 242, 141--156 (2013; Zbl 1255.65073) Full Text: DOI
Xiang, Shuhuang On fast algorithms for the evaluation of Legendre coefficients. (English) Zbl 1256.65023 Appl. Math. Lett. 26, No. 2, 194-200 (2013). MSC: 65D20 PDFBibTeX XMLCite \textit{S. Xiang}, Appl. Math. Lett. 26, No. 2, 194--200 (2013; Zbl 1256.65023) Full Text: DOI
Xiang, Shuhuang On the Optimal Rates of Convergence for Quadratures Derived from Chebyshev Points. arXiv:1308.4322 Preprint, arXiv:1308.4322 [math.NA] (2013). MSC: 65D32 65D30 BibTeX Cite \textit{S. Xiang}, ``On the Optimal Rates of Convergence for Quadratures Derived from Chebyshev Points'', Preprint, arXiv:1308.4322 [math.NA] (2013) Full Text: arXiv OA License
Xiang, Shuhuang; Bornemann, Folkmar On the convergence rates of Gauss and Clenshaw-Curtis quadrature for functions of limited regularity. (English) Zbl 1259.65059 SIAM J. Numer. Anal. 50, No. 5, 2581-2587 (2012). MSC: 65D32 41A25 41A55 PDFBibTeX XMLCite \textit{S. Xiang} and \textit{F. Bornemann}, SIAM J. Numer. Anal. 50, No. 5, 2581--2587 (2012; Zbl 1259.65059) Full Text: DOI arXiv
Xiang, Shuhuang On error bounds for orthogonal polynomial expansions and Gauss-type quadrature. (English) Zbl 1263.65027 SIAM J. Numer. Anal. 50, No. 3, 1240-1263 (2012). Reviewer: Ana-Maria Acu (Sibiu) MSC: 65D32 65D20 42C05 33C45 33F05 41A55 PDFBibTeX XMLCite \textit{S. Xiang}, SIAM J. Numer. Anal. 50, No. 3, 1240--1263 (2012; Zbl 1263.65027) Full Text: DOI
Wang, Haiyong; Xiang, Shuhuang On the convergence rates of Legendre approximation. (English) Zbl 1242.41016 Math. Comput. 81, No. 278, 861-877 (2012). Reviewer: Martin D. Buhmann (Gießen) MSC: 41A25 PDFBibTeX XMLCite \textit{H. Wang} and \textit{S. Xiang}, Math. Comput. 81, No. 278, 861--877 (2012; Zbl 1242.41016) Full Text: DOI
Xiang, Shuhuang; Chen, Xiaojun; Wang, Haiyong Error bounds for approximation in Chebyshev points. (English) Zbl 1201.65040 Numer. Math. 116, No. 3, 463-491 (2010). Reviewer: Denis Sidorov (Irkutsk) MSC: 65D32 65D30 41A50 PDFBibTeX XMLCite \textit{S. Xiang} et al., Numer. Math. 116, No. 3, 463--491 (2010; Zbl 1201.65040) Full Text: DOI
Wang, Haiyong; Xiang, Shuhuang Uniform approximations to Cauchy principal value integrals of oscillatory functions. (English) Zbl 1179.65165 Appl. Math. Comput. 215, No. 5, 1886-1894 (2009). MSC: 65T40 65D32 42A16 65T50 PDFBibTeX XMLCite \textit{H. Wang} and \textit{S. Xiang}, Appl. Math. Comput. 215, No. 5, 1886--1894 (2009; Zbl 1179.65165) Full Text: DOI