Bibliography for Lagrange Polynomial Interpolation and Approximation

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  1. Element-Free Method Based on Lagrange Polynomial
    Suetake, Y.
    Journal of Engineering Mechanics, 2002, vol. 128, no. 2, pp. 231-239, Ingenta. 
  2. The Tangent Parabola
    Russell Howell and John Mathews
    The AMATYC Review, Vol. 23, No. 1, Fall 2001, pp. 25-32.
  3. On Lagrange interpolation with equally spaced nodes.
    Revers, Michael
    Bull. Austral. Math. Soc. 62 (2000), no. 3, 357--368, MathSciNet.  
  4. The divergence of Lagrange interpolation for [Graphics:../Images/LagrangePolyBib_gr_1.gif] at equidistant nodes.
    Revers, Michael
    J. Approx. Theory 103 (2000), no. 2, 269--280, MathSciNet.  
  5. How good (or bad) is Lagrange interpolation?
    Li, Xin
    Fourier analysis, approximation theory and applications (Aligarh, 1993), 135--143, New Age, New Delhi, 1997, MathSciNet.  
  6. On Quadrature Convergence of Extended Lagrange Interpolation  
    Walter Gautschi, Shikang Li  
    Mathematics of Computation, Vol. 65, No. 215. (Jul., 1996), pp. 1249-1256, Jstor.  
  7. On Multivariate Lagrange Interpolation  
    Thomas Sauer, Yuan Xu  
    Mathematics of Computation, Vol. 64, No. 211. (Jul., 1995), pp. 1147-1170, Jstor.
  8. On the Divergence of Lagrange Interpolation with Equidistant Nodes  
    X. Li, R. N. Mohapatra  
    Proceedings of the American Mathematical Society, Vol. 118, No. 4. (Aug., 1993), pp. 1205-1212, Jstor.  
  9. On Lagrange Interpolation at Disturbed Roots of Unity  
    Charles K. Chui, Xie-Chang Shen, Lefan Zhong  
    Transactions of the American Mathematical Society, Vol. 336, No. 2. (Apr., 1993), pp. 817-830 , Jstor. 
  10. Investigation of Tangent Polynomials with a Computer Algebra System
    Russell Howell and John Mathews
    The AMATYC Review, Vol. 14, No. 1, Fall 1992, pp. 20-27.
     
  11. On Weighted Lp-Convergence of Certain Lagrange Interpolation  
    Guohua Min  
    Proceedings of the American Mathematical Society, Vol. 116, No. 4. (Dec., 1992), pp. 1081-1087 , Jstor.  
  12. Pointwise Simultaneous Convergence of Extended Lagrange Interpolation with Additional Knots  
    Giuliana Criscuolo, Giuseppe Mastroianni, Peter Vertesi  
    Mathematics of Computation, Vol. 59, No. 200. (Oct., 1992), pp. 515-531, Jstor.  
  13. Multivariate Divided Differences I: Basic Properties  
    M. Neamtu  
    SIAM Journal on Numerical Analysis, Vol. 29, No. 5. (Oct., 1992), pp. 1435-1445, Jstor.  
  14. On Kramer's Sampling Theorem Associated with General Sturm-Liouville Problems and Lagrange Interpolation  
    Ahmed I. Zayed  
    SIAM Journal on Applied Mathematics, Vol. 51, No. 2. (Apr., 1991), pp. 575-604 , Jstor.  
  15. Optimal Lebesgue Constant for Lagrange Interpolation  
    P. Vertesi  
    SIAM Journal on Numerical Analysis, Vol. 27, No. 5. (Oct., 1990), pp. 1322-1331 , Jstor.  
  16. Convergence of Extended Lagrange Interpolation  
    Giuliana Criscuolo, Giuseppe Mastroianni, Donatella Occorsio  
    Mathematics of Computation, Vol. 55, No. 191. (Jul., 1990), pp. 197-212 , Jstor.  
  17. On Lagrange Interpolation and Kramer-Type Sampling Theorems Associated with Sturm-Liouville Problems  
    Ahmed I. Zayed, Guido Hinsen, Paul L. Butzer  
    SIAM Journal on Applied Mathematics, Vol. 50, No. 3. (Jun., 1990), pp. 893-909 , Jstor.  
  18. A Remark on Divided Differences (in Notes)  
    E. T. Y. Lee  
    American Mathematical Monthly, Vol. 96, No. 7. (Aug. - Sep., 1989), pp. 618-622, Jstor.
  19. On Asymptotics for the Uniform Norms of the Lagrange Interpolation Polynomials Corresponding to Extended Chebyshev Nodes  
    R. Gunttner  
    SIAM Journal on Numerical Analysis, Vol. 25, No. 2. (Apr., 1988), pp. 461-469, Jstor.  
  20. Lagrange interpolation---divergence.
    Baker, G. B.; Mills, T. M.
    Math. Chronicle 17 (1988), 1--18, MathSciNet.  
  21. Polynomial Interpolation: Lagrange versus Newton  
    Wilhelm Werner  
    Mathematics of Computation, Vol. 43, No. 167. (Jul., 1984), pp. 205-217, Jstor.  
  22. Mean Convergence of Lagrange Interpolation. III  
    Paul Nevai  
    Transactions of the American Mathematical Society, Vol. 282, No. 2. (Apr., 1984), pp. 669-698, Jstor.  
  23. Recurrence Relations for Computing with Modified Divided Differences  
    Fred T. Krogh  
    Mathematics of Computation, Vol. 33, No. 148. (Oct., 1979), pp. 1265-1271, Jstor.  
  24. Lagrange interpolation---decline and fall?  
    Elliott, David  
    Internat. J. Math. Ed. Sci. Tech. 10 (1979), no. 1, 1--12, MathSciNet.  
  25. An introduction to analysis by Lagrange interpolation.  
    Mills, T. M.  
    Austral. Math. Soc. Gaz. 4 (1977), no. 1, 10--18, MathSciNet.  
  26. On a Class of Finite Elements Generated by Lagrange Interpolation. II  
    R. A. Nicolaides  
    SIAM Journal on Numerical Analysis, Vol. 10, No. 1. (Mar., 1973), pp. 182-189, Jstor.  
  27. On a Class of Finite Elements Generated by Lagrange Interpolation  
    R. A. Nicolaides  
    SIAM Journal on Numerical Analysis, Vol. 9, No. 3. (Sep., 1972), pp. 435-445, Jstor.  
  28. Lagrange's Interpolation Formula  
    D. A. Quadling  
    The Mathematical Gazette, Vol. L, no. 374, (December, 1966), pp. 372-375.  
  29. On Lagrange-Hermite Interpolation  
    J. F. Traub  
    Journal of the Society for Industrial and Applied Mathematics, Vol. 12, No. 4. (Dec., 1964), pp. 886-891, Jstor.
  30. Multi-Point Generalization of Newton's Divided Difference Formula  
    Herbert E. Salzer
    Proceedings of the American Mathematical Society, Vol. 13, No. 2. (Apr., 1962), pp. 210-212, Jstor.
  31. The Lagrange Interpolation Formula and Stirling Numbers  
    H. W. Gould  
    Proceedings of the American Mathematical Society, Vol. 11, No. 3. (Jun., 1960), pp. 421-425, Jstor.
  32. A Modification of the Aitken-Neville Linear Iterative Procedures for Polynomial Interpolation  
    M. C. K. Tweedie  
    Mathematical Tables and Other Aids to Computation, Vol. 8, No. 45. (Jan., 1954), pp. 13-16, Jstor.
  33. On Modified Divided Differences I  
    Gertrude Blanch  
    Mathematical Tables and Other Aids to Computation, Vol. 8, No. 45. (Jan., 1954), pp. 1-11, Jstor.
  34. A New Interpolation Formula  
    P. M. Hummel, C. L. Seebeck, Jr.  
    American Mathematical Monthly, Vol. 58, No. 6. (Jun. - Jul., 1951), pp. 383-389, Jstor.
  35. Some Applications of Aitken's Method of Interpolation (in Classroom Notes)  
    L. A. Aroian  
    American Mathematical Monthly, Vol. 55, No. 9. (Nov., 1948), pp. 569-572, Jstor.
  36. A Note on Interpolation (in Mathematical Notes)  
    P. M. Hummel  
    American Mathematical Monthly, Vol. 54, No. 4. (Apr., 1947), pp. 218-219, Jstor.
  37. An Interpolation Formula  
    E. J. McShane  
    American Mathematical Monthly, Vol. 53, No. 5. (May, 1946), pp. 259-264, Jstor.  
  38. On Divergence Properties of the Lagrange Interpolation Parabolas  
    P. Erdos  
    The Annals of Mathematics, 2nd Ser., Vol. 42, No. 1. (Jan., 1941), pp. 309-315, Jstor.  
  39. Note on an Extension of Lagrange's Formula  
    J. J. Corliss  
    American Mathematical Monthly, Vol. 45, No. 2. (Feb., 1938), pp. 106-107, Jstor.
  40. On Interpolation II: On the Distribution of the Fundamental Points of Lagrange and Hermite Interpolation  
    P. Erdos, P. Turan  
    The Annals of Mathematics, 2nd Ser., Vol. 39, No. 4. (Oct., 1938), pp. 703-724, Jstor.
  41. On the Convergence Properties of Lagrange Interpolation Based on the Zeros of Orthogonal Tchebycheff Polynomials  
    J. Shohat  
    The Annals of Mathematics, 2nd Ser., Vol. 38, No. 4. (Oct., 1937), pp. 758-769, Jstor.
  42. Note on Interpolation (in Notes)  
    Jan K. Wisniewski  
    Journal of the American Statistical Association, Vol. 25, No. 170. (Jun., 1930), pp. 203-205, Jstor.
  43. A Shortened Interpolation Formula for Certain Types of Data (in Notes)  
    E. P. Neale, D. M. Y. Sommerville  
    Journal of the American Statistical Association, Vol. 19, No. 148. (Dec., 1924), pp. 515-517, Jstor.
  44. On Taylor's Interpolation Formula as a Limiting Case of the Interpolation Formula of Lagrange (in Notes)  
    Robert E. Moritz  
    Journal of the American Statistical Association, Vol. 18, No. 142. (Jun., 1923), pp. 781-784, Jstor.
  45. A Formula of Polynomial Interpolation  
    Webster G. Simon  
    The Annals of Mathematics, 2nd Ser., Vol. 19, No. 4. (Jun., 1918), pp. 242-245, Jstor.
  46. On a Formula of Interpolation  
    E. D. Roe, Jr.  
    American Mathematical Monthly, Vol. 8, No. 1. (Jan., 1901), pp. 1-9, Jstor.  
  47. On Some Forms of Lagrange's Interpolation Formula  
    W. H. Echols  
    The Annals of Mathematics, Vol. 8, No. 1/6. (1893 - 1894), pp. 22-24, Jstor.

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2003