References
V. M. Badkov, Uniform asymptotic representations of orthogonal polynomials,Proc. Steklov Inst. Math.,164 (1985), 5–41.
A. Bellen, A note on mean convergence of Lagrange interpolation,J. Approx. Th.,33 (1981), 85–95.
G. Criscuolo and B. Della Vecchia, Extended Lagrange interpolation by zeros of Jacobi polynomials of second kind,Rend. Circ. Mat. Palermo, Suppl.33 (1993), 281–287.
G. Criscuolo, G. Mastroanni and P. Nevai, Mean convergence of the derivatives of extended Lagrange interpolation with additional nodes,Math. Nachr.,163 (1993), 73–92.
G. Criscuolo, G. Mastroanni and P. Nevai, Associated generalized Jacobi functions and polynomials, manuscript.
P. Erdős and P. Turán, On interpolation I,Annals Math.,38 (1937), 142–155.
G. Freud,Orthogonale Polynome, Birkhäuser Verlag (1969).
Ya. L. Geronimus, Polynomials orthogonal on a circle and their applications,Zap. Nauchn. Issled. Inst. Mat. Khar’kov Mat. Obsc.,19 (1948), 35–120;Amer. Math. Soc. Transl. Ser.,13 (1962), 1–78.
Ya. L. Geronimus,Polynomials Orthogonal on a Circle and Interval, Pergamon Press (1960).
Ya. L. Geronimus and B. L. Golinski, Asymptotic formulas for orthogonal polynomials,Teor. Funkcii. Funkcional Anal. i. Prizolen,1 (1965), 141–163 (in Russian).
I. P. Natanson,Constructive Function Theory, Vol. III, Ungar Publ. Co. (New York, 1965).
P. Nevai, Lagrange interpolation at zeros of orthogonal polynomials, in:Approximation Theory II, Eds.: Chui, Schumaker, Ward (1976).
P. Nevai,Orthogonal Polynomials, AMS Memoirs, 213 Amer. Math. Soc. (Providence, R. I., 1979).
D. Occorsio, Una buona matrice di nodi di interpolazione, to appear inCalcolo.
F. Peherstofer, Orthogonal polynomials inL 1-approximation,J. Approx. Theory,52 (1988), 241–268.
F. Peherstorfer, On the asymptotic behaviour of functions of the second kind and Stieltjes polynomials and on the Gauss-Kronrod quadrature formulas,J. Approx. Theory,70 (1992), 156–190.
F. Peherstorfer, On positive quadrature formulas, inNumerical Integration V (H. Braß, G. Hämmerlin, Eds.) pp. 297–313, ISNM 112, Birkhäuser (Basel, 1993).
F. Peherstorfer, On zeros of linear combinations of orthogonal polynomials,Proc. Math. Cambr.,117 (1995), 533–544.
F. Peherstorfer, Interlacing properties of zeros of orthogonal polynomials, manuscript.
J. Shohat, On mechanical quadratures in particular, with positive coefficients,Trans. Amer. Math. Soc.,42 (1937), 461–496.
J. Shohat, Application of orthogonal Tchebycheff polynomials to Lagrangean interpolation and to the general theory of polynomials,Annali di Mat. Pura Appl.,18 (1939), 201–238.
J. Szabados and P. Vértesi, A survey on a mean convergence of interpolatory processes,J. Comp. Appl. Math.,43 (1992), 3–18.
G. Szegö,Orthogonal polynomials, 4th edition, American Mathematical Society (1975).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Peherstorfer, F. Convergence of lagrange interpolation processes based on new systems of nodes. Acta Math Hung 74, 101–123 (1997). https://doi.org/10.1007/BF02697880
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02697880