Majidian, Hassan; Firouzi, Medina; Alipanah, Amjad On the stability of Filon-Clenshaw-Curtis rules. (English) Zbl 07648440 Bull. Iran. Math. Soc. 48, No. 6, 2943-2964 (2022). MSC: 65D30 33C47 PDFBibTeX XMLCite \textit{H. Majidian} et al., Bull. Iran. Math. Soc. 48, No. 6, 2943--2964 (2022; Zbl 07648440) Full Text: DOI
Costabile, F. A.; Gualtieri, M. I.; Napoli, A. Matrix calculus-based approach to orthogonal polynomial sequences. (English) Zbl 1443.42015 Mediterr. J. Math. 17, No. 4, Paper No. 118, 22 p. (2020). MSC: 42C05 11B83 33C45 PDFBibTeX XMLCite \textit{F. A. Costabile} et al., Mediterr. J. Math. 17, No. 4, Paper No. 118, 22 p. (2020; Zbl 1443.42015) Full Text: DOI
Barrio, Roberto; Du, Peibing; Jiang, Hao; Serrano, Sergio ORTHOPOLY: a library for accurate evaluation of series of classical orthogonal polynomials and their derivatives. (English) Zbl 1498.33009 Comput. Phys. Commun. 231, 146-162 (2018). MSC: 33C47 65F25 65R10 PDFBibTeX XMLCite \textit{R. Barrio} et al., Comput. Phys. Commun. 231, 146--162 (2018; Zbl 1498.33009) Full Text: DOI
Bremer, James An algorithm for the numerical evaluation of the associated Legendre functions that runs in time independent of degree and order. (English) Zbl 1395.65005 J. Comput. Phys. 360, 15-38 (2018). MSC: 65D20 33C45 PDFBibTeX XMLCite \textit{J. Bremer}, J. Comput. Phys. 360, 15--38 (2018; Zbl 1395.65005) Full Text: DOI arXiv
Plešinger, Martin; Pultarová, Ivana On the extreme eigenvalues of certain matrices of non-standard inner products of Hermite polynomials. (English) Zbl 1390.15017 Linear Algebra Appl. 546, 50-66 (2018). MSC: 15A12 15A18 15B57 33C45 PDFBibTeX XMLCite \textit{M. Plešinger} and \textit{I. Pultarová}, Linear Algebra Appl. 546, 50--66 (2018; Zbl 1390.15017) Full Text: DOI
Berriochoa, E.; Cachafeiro, A.; Amor, J. M. García An interpolation problem on the circle between Lagrange and Hermite problems. (English) Zbl 1357.41013 J. Approx. Theory 215, 118-144 (2017). Reviewer: Martin D. Buhmann (Gießen) MSC: 41A25 41A05 65D05 42C05 PDFBibTeX XMLCite \textit{E. Berriochoa} et al., J. Approx. Theory 215, 118--144 (2017; Zbl 1357.41013) Full Text: DOI
Area, Iván; Dimitrov, Dimitar K.; Godoy, Eduardo; Paschoa, Vanessa G. Approximate calculation of sums. II: Gaussian type quadrature. (English) Zbl 1343.65021 SIAM J. Numer. Anal. 54, No. 4, 2210-2227 (2016). MSC: 65D30 65H04 PDFBibTeX XMLCite \textit{I. Area} et al., SIAM J. Numer. Anal. 54, No. 4, 2210--2227 (2016; Zbl 1343.65021) Full Text: DOI
Nakatsukasa, Yuji; Noferini, Vanni On the stability of computing polynomial roots via confederate linearizations. (English) Zbl 1347.65096 Math. Comput. 85, No. 301, 2391-2425 (2016). Reviewer: José Manuel Gutiérrez Jimenez (Logrono) MSC: 65H04 65F15 PDFBibTeX XMLCite \textit{Y. Nakatsukasa} and \textit{V. Noferini}, Math. Comput. 85, No. 301, 2391--2425 (2016; Zbl 1347.65096) Full Text: DOI Link
Smoktunowicz, Alicja; Smoktunowicz, Agata; Pawelec, Ewa The three-term recursion for Chebyshev polynomials is mixed forward-backward stable. (English) Zbl 1326.65031 Numer. Algorithms 69, No. 4, 785-794 (2015). Reviewer: Yuri A. Farkov (Moscow) MSC: 65D20 65G50 65H04 33C45 65Q30 PDFBibTeX XMLCite \textit{A. Smoktunowicz} et al., Numer. Algorithms 69, No. 4, 785--794 (2015; Zbl 1326.65031) Full Text: DOI arXiv
Murashige, Sunao; Tanaka, Ken’ichiro A new method of convergence acceleration of series expansion for analytic functions in the complex domain. (English) Zbl 1321.30002 Japan J. Ind. Appl. Math. 32, No. 1, 95-117 (2015). Reviewer: Yuri A. Farkov (Moscow) MSC: 30B10 30E10 42C05 65B99 PDFBibTeX XMLCite \textit{S. Murashige} and \textit{K. Tanaka}, Japan J. Ind. Appl. Math. 32, No. 1, 95--117 (2015; Zbl 1321.30002) Full Text: DOI
Olver, Sheehan; Townsend, Alex A fast and well-conditioned spectral method. (English) Zbl 1273.65182 SIAM Rev. 55, No. 3, 462-489 (2013). MSC: 65N35 65L10 33C45 PDFBibTeX XMLCite \textit{S. Olver} and \textit{A. Townsend}, SIAM Rev. 55, No. 3, 462--489 (2013; Zbl 1273.65182) Full Text: DOI arXiv
Barrio, Roberto; Jiang, Hao; Serrano, Sergio A general condition number for polynomials. (English) Zbl 1273.65036 SIAM J. Numer. Anal. 51, No. 2, 1280-1294 (2013). Reviewer: Kai Diethelm (Braunschweig) MSC: 65D20 41A10 65G50 PDFBibTeX XMLCite \textit{R. Barrio} et al., SIAM J. Numer. Anal. 51, No. 2, 1280--1294 (2013; Zbl 1273.65036) Full Text: DOI Link
Costabile, F. A.; Longo, E. A determinantal approach to Appell polynomials. (English) Zbl 1200.33020 J. Comput. Appl. Math. 234, No. 5, 1528-1542 (2010). Reviewer: Thomas Stoll (Marseille) MSC: 33C65 33C45 11B83 65F40 PDFBibTeX XMLCite \textit{F. A. Costabile} and \textit{E. Longo}, J. Comput. Appl. Math. 234, No. 5, 1528--1542 (2010; Zbl 1200.33020) Full Text: DOI
Bueno Cachadina, Maria Isabel; Deaño, Alfredo; Tavernetti, Edward A new algorithm for computing the Geronimus transformation with large shifts. (English) Zbl 1191.65039 Numer. Algorithms 54, No. 1, 101-139 (2010). Reviewer: Hang Lau (Montréal) MSC: 65F30 42C05 65Q30 65F22 PDFBibTeX XMLCite \textit{M. I. Bueno Cachadina} et al., Numer. Algorithms 54, No. 1, 101--139 (2010; Zbl 1191.65039) Full Text: DOI
Barrio, Roberto; Peña, Juan Manuel; Sauer, Tomas Three term recurrence for the evaluation of multivariate orthogonal polynomials. (English) Zbl 1190.33011 J. Approx. Theory 162, No. 2, 407-420 (2010). Reviewer: Alicia Cachafeiro López (Vigo) MSC: 33C45 33C50 PDFBibTeX XMLCite \textit{R. Barrio} et al., J. Approx. Theory 162, No. 2, 407--420 (2010; Zbl 1190.33011) Full Text: DOI
Golub, Gene H.; Meurant, Gérard Matrices, moments and quadrature with applications. (English) Zbl 1217.65056 Princeton Series in Applied Mathematics. Princeton, NJ: Princeton University Press (ISBN 978-0-691-14341-5/hbk; 978-1-400-83388-7/ebook). xi, 363 p. (2010). Reviewer: Liu Xinguo (Qingdao) MSC: 65D32 65F22 65F15 65F20 65-01 15-01 65F10 65D10 41A55 42C05 PDFBibTeX XMLCite \textit{G. H. Golub} and \textit{G. Meurant}, Matrices, moments and quadrature with applications. Princeton, NJ: Princeton University Press (2010; Zbl 1217.65056)
Knizhnerman, Leonid Sensitivity of the Lanczos recurrence to Gaussian quadrature data: how malignant can small weights be? (English) Zbl 1186.65031 J. Comput. Appl. Math. 233, No. 5, 1238-1244 (2010). Reviewer: Robert Plato (Siegen) MSC: 65D32 42C05 65F18 41A55 PDFBibTeX XMLCite \textit{L. Knizhnerman}, J. Comput. Appl. Math. 233, No. 5, 1238--1244 (2010; Zbl 1186.65031) Full Text: DOI
Costabile, F. A.; Serpe, A. An algebraic approach to Lidstone polynomials. (English) Zbl 1204.33014 Appl. Math. Lett. 20, No. 4, 387-390 (2007). MSC: 33C47 33E20 PDFBibTeX XMLCite \textit{F. A. Costabile} and \textit{A. Serpe}, Appl. Math. Lett. 20, No. 4, 387--390 (2007; Zbl 1204.33014) Full Text: DOI
Bueno, María I.; Dopico, Froilán M. A more accurate algorithm for computing the Christoffel transformation. (English) Zbl 1120.65050 J. Comput. Appl. Math. 205, No. 1, 567-582 (2007). Reviewer: Rémi Vaillancourt (Ottawa) MSC: 65F30 65G50 65F35 42C05 PDFBibTeX XMLCite \textit{M. I. Bueno} and \textit{F. M. Dopico}, J. Comput. Appl. Math. 205, No. 1, 567--582 (2007; Zbl 1120.65050) Full Text: DOI
Peña, Juan Manuel; Sauer, Tomas Efficient polynomial reduction. (English) Zbl 1109.13024 Adv. Comput. Math. 26, No. 1-3, 323-336 (2007). MSC: 13P10 42C05 41A10 65D15 PDFBibTeX XMLCite \textit{J. M. Peña} and \textit{T. Sauer}, Adv. Comput. Math. 26, No. 1--3, 323--336 (2007; Zbl 1109.13024) Full Text: DOI
Barrio, R.; Peña, J. M. Evaluation of the derivative of a polynomial in Bernstein form. (English) Zbl 1086.65014 Appl. Math. Comput. 167, No. 1, 125-142 (2005). Reviewer: Luigi Gatteschi (Torino) MSC: 65D25 65D18 65D17 12Y05 26C05 PDFBibTeX XMLCite \textit{R. Barrio} and \textit{J. M. Peña}, Appl. Math. Comput. 167, No. 1, 125--142 (2005; Zbl 1086.65014) Full Text: DOI
Barrio, R.; Serrano, S. Generation and evaluation of orthogonal polynomials in discrete Sobolev spaces. II: numerical stability. (English) Zbl 1073.65018 J. Comput. Appl. Math. 181, No. 2, 299-320 (2005). MSC: 65D20 42C05 65G50 42C10 65T40 PDFBibTeX XMLCite \textit{R. Barrio} and \textit{S. Serrano}, J. Comput. Appl. Math. 181, No. 2, 299--320 (2005; Zbl 1073.65018) Full Text: DOI
Barrio, R.; Peña, J. M. Numerical evaluation of the \(p\)th derivative of Jacobi series. (English) Zbl 1018.65031 Appl. Numer. Math. 43, No. 4, 335-357 (2002). Reviewer: C.L.Koul (Jaipur) MSC: 65D25 65D20 33C45 33F05 PDFBibTeX XMLCite \textit{R. Barrio} and \textit{J. M. Peña}, Appl. Numer. Math. 43, No. 4, 335--357 (2002; Zbl 1018.65031) Full Text: DOI
Barrio, Roberto Rounding error bounds for the Clenshaw and Forsythe algorithms for the evaluation of orthogonal polynomial series. (English) Zbl 0998.65033 J. Comput. Appl. Math. 138, No. 2, 185-204 (2002). Reviewer: Luigi Gatteschi (Torino) MSC: 65D20 65G50 33C45 42C05 PDFBibTeX XMLCite \textit{R. Barrio}, J. Comput. Appl. Math. 138, No. 2, 185--204 (2002; Zbl 0998.65033) Full Text: DOI
Barrio, R. Stability of parallel algorithms to evaluate Chebyshev series. (English) Zbl 1002.65002 Comput. Math. Appl. 41, No. 10-11, 1365-1377 (2001). Reviewer: N.Ţăndăreanu (Craiova) MSC: 65B10 65G50 65Y05 65D20 33C45 33F05 PDFBibTeX XMLCite \textit{R. Barrio}, Comput. Math. Appl. 41, No. 10--11, 1365--1377 (2001; Zbl 1002.65002) Full Text: DOI