Bibliography for Newton Interpolation Polynomial

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  1. Matrix newton interpolation and progressive 3D imaging: PC-based computation
    Defez, E.; Law, A.; Villanueva-Oller, J.; Villanueva, R. J.
    Mathematical and Computer Modelling, 2002, vol. 35, no. ER3-4, pp. 303-322, Ingenta. 
  2. The Tangent Parabola
    Russell Howell and John Mathews
    The AMATYC Review, Vol. 23, No. 1, Fall 2001, pp. 25-32.
      
  3. Convergence of Newton's method for convex best interpolation
    Dontchev, A. L.; Qi, H.; Qi, L.
    Numerische Mathematik, 2001, vol. 87, no. 3, pp. 435-456, Ingenta.   
  4. Forward error analysis of Neville elimination. (Spanish)
    Alonso, Pedro; Gasca, Mariano; Peña, Juan Manuel
    Rev. R. Acad. Cienc. Exactas Fís. Nat. (Esp.) 92 (1998), no. 1, 1--8, Math. Sci. Net.
  5. Pipelined algorithm for Newton's divided difference interpolation.
    Al-Ayyoub, A. E.
    Comput. & Structures 58 (1996), no. 4, 689--701, Math. Sci. Net.
  6. 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.
  7. Multivariate Divided Differences I: Basic Properties  
    M. Neamtu  
    SIAM Journal on Numerical Analysis, Vol. 29, No. 5. (Oct., 1992), pp. 1435-1445, Jstor.  
  8. Newton Interpolation in Fejer and Chebyshev Points  
    Bernd Fischer, Lothar Reichel  
    Mathematics of Computation, Vol. 53, No. 187. (Jul., 1989), pp. 265-278, Jstor.
  9. 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.
  10. Divided Differences, Shift Transformations and Larkin's Root Finding Method  
    A. Neumaier, A. Schafer  
    Mathematics of Computation, Vol. 45, No. 171. (Jul., 1985), pp. 181-196, Jstor.  
  11. Polynomial Interpolation: Lagrange versus Newton  
    Wilhelm Werner  
    Mathematics of Computation, Vol. 43, No. 167. (Jul., 1984), pp. 205-217, Jstor.  
  12. Accurate Computation of Divided Differences of the Exponential Function  
    A. McCurdy, K. C. Ng, B. N. Parlett  
    Mathematics of Computation, Vol. 43, No. 168. (Oct., 1984), pp. 501-528, Jstor.  
  13. Divided Differences Associated with Reversible Systems in R^2  
    J. I. Maeztu  
    SIAM Journal on Numerical Analysis, Vol. 19, No. 5. (Oct., 1982), pp. 1032-1040, Jstor.  
  14. Orthogonal Newton polynomials.
    de Branges, Louis; Trutt, David
    Adv. in Math. 37 (1980), no. 3, 251--271, Math. Sci. Net.
  15. Recurrence Relations for Computing with Modified Divided Differences  
    Fred T. Krogh  
    Mathematics of Computation, Vol. 33, No. 148. (Oct., 1979), pp. 1265-1271, Jstor.  
  16. Neville's and Romberg's Processes: A Fresh Appraisal with Extensions  
    J. C. P. Miller  
    Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 263, No. 1144. (Dec. 24, 1968), pp. 525-562, Jstor.
  17. 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.
  18. High Accuracy Quadrature Formulas From Divided Differences With Repeated Arguments  
    K. S. Kunz  
    Mathematical Tables and Other Aids to Computation, Vol. 10, No. 54. (Apr., 1956), pp. 87-90, Jstor.  
  19. 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.
  20. On Modified Divided Differences II  
    Gertrude Blanch  
    Mathematical Tables and Other Aids to Computation, Vol. 8, No. 46. (Apr., 1954), pp. 67-75, Jstor.
  21. On Modified Divided Differences I  
    Gertrude Blanch  
    Mathematical Tables and Other Aids to Computation, Vol. 8, No. 45. (Jan., 1954), pp. 1-11, Jstor.
  22. A Note on Interpolation (in Mathematical Notes)  
    P. M. Hummel  
    American Mathematical Monthly, Vol. 54, No. 4. (Apr., 1947), pp. 218-219, Jstor.
  23. An Interpolation Formula  
    E. J. McShane  
    American Mathematical Monthly, Vol. 53, No. 5. (May, 1946), pp. 259-264, Jstor.  
  24. 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.

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2003