Berriochoa, E.; Cachafeiro, A.; García-Amor, J.; García Rábade, H. The Gibbs-Wilbraham phenomenon in the approximation of \(| x |\) by using Lagrange interpolation on the Chebyshev-Lobatto nodal systems. (English) Zbl 1524.41005 J. Comput. Appl. Math. 414, Article ID 114403, 22 p. (2022). MSC: 41A05 42C05 65D05 PDFBibTeX XMLCite \textit{E. Berriochoa} et al., J. Comput. Appl. Math. 414, Article ID 114403, 22 p. (2022; Zbl 1524.41005) Full Text: DOI
Berriochoa, E.; Cachafeiro, A.; García Amor, J. M. Gibbs-Wilbraham phenomenon on Lagrange interpolation based on analytic weights on the unit circle. (English) Zbl 1428.41002 J. Comput. Appl. Math. 365, Article ID 112376, 17 p. (2020). MSC: 41A05 65D05 PDFBibTeX XMLCite \textit{E. Berriochoa} et al., J. Comput. Appl. Math. 365, Article ID 112376, 17 p. (2020; Zbl 1428.41002) Full Text: DOI
Berriochoa, E.; Cachafeiro, A.; Marcellán, F. Szegő transformation and zeros of analytic perturbations of Chebyshev weights. (English) Zbl 1404.30005 J. Math. Anal. Appl. 470, No. 1, 571-583 (2019). MSC: 30C15 33C45 PDFBibTeX XMLCite \textit{E. Berriochoa} et al., J. Math. Anal. Appl. 470, No. 1, 571--583 (2019; Zbl 1404.30005) Full Text: DOI
Berriochoa, E.; Cachafeiro, A.; García Amor, J. M. Gibbs-Wilbraham oscillation related to an Hermite interpolation problem on the unit circle. (English) Zbl 1460.41001 J. Comput. Appl. Math. 344, 657-675 (2018). MSC: 41A05 42C05 65D05 PDFBibTeX XMLCite \textit{E. Berriochoa} et al., J. Comput. Appl. Math. 344, 657--675 (2018; Zbl 1460.41001) Full Text: DOI
Berriochoa, Elías; Cachafeiro, Alicia; García-Amor, José M. Algorithms, convergence and rate of convergence for an interpolation model between Lagrange and Hermite. (English) Zbl 1390.41002 Result. Math. 73, No. 1, Paper No. 40, 30 p. (2018). MSC: 41A05 65D05 42C05 PDFBibTeX XMLCite \textit{E. Berriochoa} et al., Result. Math. 73, No. 1, Paper No. 40, 30 p. (2018; Zbl 1390.41002) 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
Berriochoa, E.; Cachafeiro, A. On the asymptotic constant for the rate of Hermite-Fejér convergence on Chebyshev nodes. (English) Zbl 1363.41001 Acta Math. Hung. 147, No. 1, 32-45 (2015). Reviewer: Adhemar Bultheel (Leuven) MSC: 41A05 65D05 33C45 PDFBibTeX XMLCite \textit{E. Berriochoa} and \textit{A. Cachafeiro}, Acta Math. Hung. 147, No. 1, 32--45 (2015; Zbl 1363.41001) Full Text: DOI
Berriochoa, E.; Cachafeiro, A.; Díaz, J. Convergence of Hermite interpolants on the circle using two derivatives. (English) Zbl 1312.41004 J. Comput. Appl. Math. 284, 58-68 (2015). MSC: 41A05 42A15 65D05 42C05 PDFBibTeX XMLCite \textit{E. Berriochoa} et al., J. Comput. Appl. Math. 284, 58--68 (2015; Zbl 1312.41004) Full Text: DOI
Berriochoa, Elías; Cachafeiro, Alicia; García-Amor, José M. An extension of Fejér’s condition for Hermite interpolation. (English) Zbl 1276.42006 Complex Anal. Oper. Theory 6, No. 3, 651-664 (2012). MSC: 42A15 33C45 26D20 PDFBibTeX XMLCite \textit{E. Berriochoa} et al., Complex Anal. Oper. Theory 6, No. 3, 651--664 (2012; Zbl 1276.42006) Full Text: DOI
Berriochoa, E.; Cachafeiro, A.; Martínez, E. About measures and nodal systems for which the Hermite interpolants uniformly converge to continuous functions on the circle and interval. (English) Zbl 1248.41002 Appl. Math. Comput. 218, No. 9, 4813-4824 (2012). Reviewer: Martin D. Buhmann (Gießen) MSC: 41A05 PDFBibTeX XMLCite \textit{E. Berriochoa} et al., Appl. Math. Comput. 218, No. 9, 4813--4824 (2012; Zbl 1248.41002) Full Text: DOI
Berriochoa, E.; Cachafeiro, A.; García-Amor, J. Complex measures having quadrature formulae with optimal exactness. (English) Zbl 1240.33011 Acta Math. Hung. 126, No. 1-2, 51-64 (2010). MSC: 33C47 42C05 65D32 PDFBibTeX XMLCite \textit{E. Berriochoa} et al., Acta Math. Hung. 126, No. 1--2, 51--64 (2010; Zbl 1240.33011) Full Text: DOI
Berriochoa, Elías; Cachafeiro, Alicia Algorithms for solving Hermite interpolation problems using the fast Fourier transform. (English) Zbl 1215.33009 J. Comput. Appl. Math. 235, No. 4, 882-894 (2010). Reviewer: Valery V. Karachik (Chelyabinsk) MSC: 33C47 65D05 33C52 65T50 65D15 65T40 PDFBibTeX XMLCite \textit{E. Berriochoa} and \textit{A. Cachafeiro}, J. Comput. Appl. Math. 235, No. 4, 882--894 (2010; Zbl 1215.33009) Full Text: DOI
Berriochoa, E.; Cachafeiro, A.; García-Amor, J. Quadrature rules for polynomial modifications of Bernstein measures exact for analytic functions. (English) Zbl 1232.33011 Integral Transforms Spec. Funct. 21, No. 5-6, 409-422 (2010). MSC: 33C45 33C47 42C05 42C10 65D32 PDFBibTeX XMLCite \textit{E. Berriochoa} et al., Integral Transforms Spec. Funct. 21, No. 5--6, 409--422 (2010; Zbl 1232.33011) Full Text: DOI
Berriochoa, E.; Cachafeiro, A.; García-Amor, J. A bi-orthogonal system of trigonometric functions. (English) Zbl 1207.33016 Integral Transforms Spec. Funct. 21, No. 1-2, 57-74 (2010). Reviewer: Jaebum Sohn (Seoul) MSC: 33C47 42C05 PDFBibTeX XMLCite \textit{E. Berriochoa} et al., Integral Transforms Spec. Funct. 21, No. 1--2, 57--74 (2010; Zbl 1207.33016) Full Text: DOI
Berriochoa, E.; Cachafeiro, A.; García Amor, J. Characterizing the measures on the unit circle with exact quadrature formulas in the space of polynomials. (English) Zbl 1189.33011 Comput. Math. Appl. 58, No. 7, 1370-1382 (2009). MSC: 33C45 65D30 PDFBibTeX XMLCite \textit{E. Berriochoa} et al., Comput. Math. Appl. 58, No. 7, 1370--1382 (2009; Zbl 1189.33011) Full Text: DOI
Berriochoa, E.; Cachafeiro, A. Characterizing curves satisfying the Gauss-Christoffel theorem. (English) Zbl 1180.33012 J. Comput. Appl. Math. 233, No. 3, 630-633 (2009). Reviewer: Som Prakash Goyal (Jaipur) MSC: 33C47 41A55 42C05 PDFBibTeX XMLCite \textit{E. Berriochoa} and \textit{A. Cachafeiro}, J. Comput. Appl. Math. 233, No. 3, 630--633 (2009; Zbl 1180.33012) Full Text: DOI
Berriochoa, Elías; Cachafeiro, Alicia; García-Amor, José M.; Marcellán, Francisco New quadrature rules for Bernstein measures on the interval \([-1,1]\). (English) Zbl 1176.33016 ETNA, Electron. Trans. Numer. Anal. 30, 278-290 (2008). MSC: 33C47 42C05 PDFBibTeX XMLCite \textit{E. Berriochoa} et al., ETNA, Electron. Trans. Numer. Anal. 30, 278--290 (2008; Zbl 1176.33016) Full Text: EuDML EMIS
Berriochoa, E.; Cachafeiro, A.; García-Amor, J. About a system of anti-periodic trigonometric functions. (English) Zbl 1155.42300 Comput. Math. Appl. 56, No. 6, 1526-1537 (2008). MSC: 42A05 PDFBibTeX XMLCite \textit{E. Berriochoa} et al., Comput. Math. Appl. 56, No. 6, 1526--1537 (2008; Zbl 1155.42300) Full Text: DOI
Berriochoa, E.; Cachafeiro, A. Nodal systems with maximal domain of exactness for Gaussian quadrature formulas. (English) Zbl 1135.33006 J. Comput. Appl. Math. 212, No. 2, 272-281 (2008). MSC: 33C47 42C05 PDFBibTeX XMLCite \textit{E. Berriochoa} and \textit{A. Cachafeiro}, J. Comput. Appl. Math. 212, No. 2, 272--281 (2008; Zbl 1135.33006) Full Text: DOI
Berriochoa, Elías; Cachafeiro, Alicia; García-Amor, José A system of biorthogonal trigonometric polynomials. (English) Zbl 1214.42040 Elaydi, S. (ed.) et al., Difference equations, special functions and orthogonal polynomials. Proceedings of the international conference, Munich, Germany, July 25–30, 2005. Hackensack, NJ: World Scientific (ISBN 978-981-270-643-0/hbk). 80-89 (2007). MSC: 42C05 PDFBibTeX XMLCite \textit{E. Berriochoa} et al., in: Difference equations, special functions and orthogonal polynomials. Proceedings of the international conference, Munich, Germany, July 25--30, 2005. Hackensack, NJ: World Scientific. 80--89 (2007; Zbl 1214.42040)
Berriochoa, E.; Cachafeiro, A.; Marcellán, F. A new numerical quadrature formula on the unit circle. (English) Zbl 1126.65023 Numer. Algorithms 44, No. 4, 391-401 (2007). Reviewer: Manfred Tasche (Rostock) MSC: 65D32 33C47 42C05 41A55 PDFBibTeX XMLCite \textit{E. Berriochoa} et al., Numer. Algorithms 44, No. 4, 391--401 (2007; Zbl 1126.65023) Full Text: DOI Link
Berriochoa, E.; Cachafeiro, A.; Garcia-Amor, J. M. Quasi-orthogonality properties and orthogonality with respect to the Chebyshev perturbation of a Bernstein measure. (English) Zbl 1130.33003 Integral Transforms Spec. Funct. 17, No. 7, 485-497 (2006). Reviewer: Marcel G. de Bruin (Haarlem) MSC: 33C47 42C05 PDFBibTeX XMLCite \textit{E. Berriochoa} et al., Integral Transforms Spec. Funct. 17, No. 7, 485--497 (2006; Zbl 1130.33003) Full Text: DOI
Berriochoa, E.; Cachafeiro, A.; Garcia-Amor, J. Asymptotics on the support for Sobolev orthogonal polynomials on a bounded interval. (English) Zbl 1080.42023 Comput. Math. Appl. 50, No. 3-4, 381-391 (2005). MSC: 42C05 PDFBibTeX XMLCite \textit{E. Berriochoa} et al., Comput. Math. Appl. 50, No. 3--4, 381--391 (2005; Zbl 1080.42023) Full Text: DOI
Berriochoa, E.; Cachafeiro, A.; Garcia-Amor, J. M. A characterization of the four Chebyshev orthogonal families. (English) Zbl 1082.42014 Int. J. Math. Math. Sci. 2005, No. 13, 2071-2079 (2005). Reviewer: Marcel G. de Bruin (Haarlem) MSC: 42C05 33C45 PDFBibTeX XMLCite \textit{E. Berriochoa} et al., Int. J. Math. Math. Sci. 2005, No. 13, 2071--2079 (2005; Zbl 1082.42014) Full Text: DOI EuDML
Berriochoa, E.; Cachafeiro, A.; García-Amor, J. Connections between interval and unit circle for Sobolev orthogonal polynomials. Strong asymptotics on the real line. (English) Zbl 1076.42016 Acta Appl. Math. 86, No. 3, 221-236 (2005). Reviewer: Andrei Martínez Finkelshtein (Almeria) MSC: 42C05 33C47 PDFBibTeX XMLCite \textit{E. Berriochoa} et al., Acta Appl. Math. 86, No. 3, 221--236 (2005; Zbl 1076.42016) Full Text: DOI
Berriochoa, E.; Cachafeiro, A.; Garcia-Amor, J. M. Asymptotic properties of Chebyshev-Sobolev orthogonal polynomials. (English) Zbl 1060.42016 J. Comput. Appl. Math. 178, No. 1-2, 63-74 (2005). MSC: 42C05 33C47 PDFBibTeX XMLCite \textit{E. Berriochoa} et al., J. Comput. Appl. Math. 178, No. 1--2, 63--74 (2005; Zbl 1060.42016) Full Text: DOI
Berriochoa, E.; Cachafeiro, A.; García-Amor, J. Connection between orthogonal polynomials on the unit circle and bounded interval. (English) Zbl 1066.33009 J. Comput. Appl. Math. 177, No. 1, 205-223 (2005). Reviewer: Wolfram Koepf (Kassel) MSC: 33C47 42C05 PDFBibTeX XMLCite \textit{E. Berriochoa} et al., J. Comput. Appl. Math. 177, No. 1, 205--223 (2005; Zbl 1066.33009) Full Text: DOI
Berriochoa, E.; Cachafeiro, A. Extension inside the disk of asymptotics for Sobolev orthogonal polynomials. (English) Zbl 1044.42023 Comput. Math. Appl. 46, No. 8-9, 1263-1272 (2003). MSC: 42C05 30C10 33C45 PDFBibTeX XMLCite \textit{E. Berriochoa} and \textit{A. Cachafeiro}, Comput. Math. Appl. 46, No. 8--9, 1263--1272 (2003; Zbl 1044.42023) Full Text: DOI
Berriochoa, E.; Cachafeiro, A. A necessary condition for the extension of Szegö’s asymptotics inside the disk in the Sobolev case. (English) Zbl 1014.42018 J. Comput. Appl. Math. 153, No. 1-2, 73-78 (2003). MSC: 42C05 33C47 PDFBibTeX XMLCite \textit{E. Berriochoa} and \textit{A. Cachafeiro}, J. Comput. Appl. Math. 153, No. 1--2, 73--78 (2003; Zbl 1014.42018) Full Text: DOI
Berriochoa, E.; Cachafeiro, A. On the strong asymptotics for Sobolev orthogonal polynomials on the circle. (English) Zbl 1015.42017 Constructive Approximation 19, No. 2, 299-307 (2003). Reviewer: Francisco Pérez Acosta (La Laguna) MSC: 42C05 33C47 PDFBibTeX XMLCite \textit{E. Berriochoa} and \textit{A. Cachafeiro}, Constr. Approx. 19, No. 2, 299--307 (2003; Zbl 1015.42017) Full Text: DOI
Berriochoa, E.; Cachafeiro, A. Differential properties for a class of Sobolev orthogonal polynomials. (English) Zbl 1058.33007 J. Comput. Appl. Math. 146, No. 2, 361-372 (2002). MSC: 33C45 42C05 PDFBibTeX XMLCite \textit{E. Berriochoa} and \textit{A. Cachafeiro}, J. Comput. Appl. Math. 146, No. 2, 361--372 (2002; Zbl 1058.33007) Full Text: DOI
Berriochoa, E.; Cachafeiro, A. Asymptotic behavior inside the disk for Lebesgue Sobolev orthogonal polynomials. (English) Zbl 1007.42017 J. Inequal. Appl. 7, No. 3, 379-392 (2002). Reviewer: Francisco Perez Acosta (La Laguna) MSC: 42C05 PDFBibTeX XMLCite \textit{E. Berriochoa} and \textit{A. Cachafeiro}, J. Inequal. Appl. 7, No. 3, 379--392 (2002; Zbl 1007.42017) Full Text: DOI
Berriochoa, E.; Cachafeiro, A. Strong asymptotics inside the unit disk for Sobolev orthogonal polynomials. (English) Zbl 1229.33021 Comput. Math. Appl. 44, No. 1-2, 253-261 (2002). MSC: 33C47 42C05 PDFBibTeX XMLCite \textit{E. Berriochoa} and \textit{A. Cachafeiro}, Comput. Math. Appl. 44, No. 1--2, 253--261 (2002; Zbl 1229.33021) Full Text: DOI
Berriochoa, Elías; Cachafeiro, Alicia Szegő’s asymptotic theory for Sobolev orthogonal polynomials over the unit disk. (Spanish. English summary) Zbl 1253.42016 Español, Luis (ed.) et al., Margarita mathematica en memoria de José Javier (Chicho) Guadalupe Hernández. Logroño: Universidad de la Rioja, Servicio de Publicaciones (ISBN 84-95301-56-3/hbk). 577-594 (2001). MSC: 42C05 41A60 PDFBibTeX XMLCite \textit{E. Berriochoa} and \textit{A. Cachafeiro}, in: Margarita mathematica en memoria de José Javier (Chicho) Guadalupe Hernández. Logroño: Universidad de la Rioja, Servicio de Publicaciones. 577--594 (2001; Zbl 1253.42016) Full Text: EMIS
Berriochoa, E.; Cachafeiro, A.; Marcellán, F. Differential properties for Sobolev orthogonality on the unit circle. (English) Zbl 0990.42006 J. Comput. Appl. Math. 133, No. 1-2, 231-239 (2001). MSC: 42C05 PDFBibTeX XMLCite \textit{E. Berriochoa} et al., J. Comput. Appl. Math. 133, No. 1--2, 231--239 (2001; Zbl 0990.42006) Full Text: DOI
Berriochoa, E.; Cachafeiro, A. Polynomials with minimal norm and new results in Szegö’s theory. (English) Zbl 1021.33009 Complex Variables, Theory Appl. 43, No. 2, 151-167 (2000). MSC: 33C45 42C05 PDFBibTeX XMLCite \textit{E. Berriochoa} and \textit{A. Cachafeiro}, Complex Variables, Theory Appl. 43, No. 2, 151--167 (2000; Zbl 1021.33009) Full Text: DOI
Berriochoa, E.; Cachafeiro, A. Bernstein-Szegö-Lebesgue-Sobolev orthogonal polynomials on the unit circle. (English) Zbl 0966.42015 J. Difference Equ. Appl. 6, No. 6, 719-737 (2000). MSC: 42C05 33C47 PDFBibTeX XMLCite \textit{E. Berriochoa} and \textit{A. Cachafeiro}, J. Difference Equ. Appl. 6, No. 6, 719--737 (2000; Zbl 0966.42015) Full Text: DOI
Aptekarev, A.; Berriochoa, E.; Cachafeiro, A. On a characeterization of integrability for the reciprocal weight of orthogonal polynomials on the circle. (English) Zbl 0961.33010 Acta Appl. Math. 61, No. 1-3, 81-86 (2000). Reviewer: Josefina Alvarez (Las Cruces) MSC: 33C47 42C05 PDFBibTeX XMLCite \textit{A. Aptekarev} et al., Acta Appl. Math. 61, No. 1--3, 81--86 (2000; Zbl 0961.33010) Full Text: DOI
Berriochoa, E.; Cachafeiro, A.; Marcellán, F. A study of the generalized Christoffel functions with applications. (English) Zbl 0965.42015 Methods Appl. Anal. 6, No. 3, 327-336 (1999). Reviewer: Walter Van Assche (Leuven) MSC: 42C05 PDFBibTeX XMLCite \textit{E. Berriochoa} et al., Methods Appl. Anal. 6, No. 3, 327--336 (1999; Zbl 0965.42015) Full Text: DOI
Aptekarev, A.; Berriochoa, E.; Cachafeiro, A. Strong asymptotics for the continuous Sobolev orthogonal polynomials on the unit circle. (English) Zbl 0934.42017 J. Approximation Theory 100, No. 2, 381-391 (1999). Reviewer: Wiesław Pleśniak (Kraków) MSC: 42C05 30C45 PDFBibTeX XMLCite \textit{A. Aptekarev} et al., J. Approx. Theory 100, No. 2, 381--391 (1999; Zbl 0934.42017) Full Text: DOI
Berriochoa, E.; Cachafeiro, A. Continuous Sobolev inner products on the unit circle: Canonical models. (English) Zbl 0947.42018 Rend. Mat. Appl., VII. Ser. 19, No. 1, 89-106 (1999). Reviewer: Andrei Martínez Finkelshtein (Almeria) MSC: 42C05 PDFBibTeX XMLCite \textit{E. Berriochoa} and \textit{A. Cachafeiro}, Rend. Mat. Appl., VII. Ser. 19, No. 1, 89--106 (1999; Zbl 0947.42018)
Berriochoa, E.; Cachafeiro, A. A family of Sobolev orthogonal polynomials on the unit circle. (English) Zbl 0952.42013 J. Comput. Appl. Math. 105, No. 1-2, 163-173 (1999). Reviewer: Andrei Martínez Finkelshtein (Almeria) MSC: 42C05 33C45 PDFBibTeX XMLCite \textit{E. Berriochoa} and \textit{A. Cachafeiro}, J. Comput. Appl. Math. 105, No. 1--2, 163--173 (1999; Zbl 0952.42013) Full Text: DOI
Berriochoa, E.; Cachafeiro, A. Lebesgue Sobolev orthogonality on the unit circle. (English) Zbl 0933.42011 J. Comput. Appl. Math. 96, No. 1, 27-34 (1998). Reviewer: M.G.de Bruin (Delft) MSC: 42C05 PDFBibTeX XMLCite \textit{E. Berriochoa} and \textit{A. Cachafeiro}, J. Comput. Appl. Math. 96, No. 1, 27--34 (1998; Zbl 0933.42011) Full Text: DOI