Bibliography for Aitken's and Neville's Interpolation Methods

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  1. Neville elimination: A study of the efficiency using checkerboard partitioning  
    Alonso, Pedro; Cortina, Raquel; Diaz, Irene; Ranilla, Jose
    Linear Algebra and Its Applications, v 393, n 1-3, Dec 1, 2004, Positivity in Linear Algebra, p 3-14, Compendex.  
  2. On the generalized inverse Neville-type matrix-valued rational interpolants
    Chen, Zhibing   
    Journal of Computational Mathematics, v 21, n 2, March, 2003, p 157-166, Compendex.
  3. Extrapolation and the Bulirsch-Stoer algorithm
    Monroe, James L.   
    Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, v 65, n 6 2, June, 2002, p 066116/1-066116/8, Compendex.
  4. A PLU-factorization of rectangular matrices by the Neville elimination  
    Gasso M.; Torregrosa J.R.  
    Linear Algebra and its Applications, 15 December 2002, vol. 357, no. 1, pp. 163-171(9), Ingenta.  
  5. Romberg quadrature using the Bulirsch sequence   
    Fischer, J.-W.
    Numer. Math.  90  (2002),  no. 3, 509--519, MathSciNet.  
  6. Neville's formula for bivariate vector-valued rational interpolants. (Chinese)
    Chen, Zhi Bing
    J. Numer. Methods Comput. Appl. 23 (2002), no. 1, 52--56, MathSciNet.  
  7. Bivariate Neville-type vector-valued rational interpolants over rectangular grids. (Chinese)
    Chen, Zhi Bing
    Math. Numer. Sin. 24 (2002), no. 1, 67--76, MathSciNet.  
  8. The Aitken-Neville scheme in several variables.
    Sauer, Thomas; Xu, Yuesheng
    Approximation theory, X (St. Louis, MO, 2001), 353--366, Innov. Appl. Math., Vanderbilt Univ. Press, Nashville, TN, 2002, MathSciNet.  
  9. One-parameter family of Neville-Aitken algorithm on q-triangle.
    Yahaya, Daud; Phillips, G. M.
    Bull. Malays. Math. Sci. Soc. (2) 23 (2000), no. 2, 107--115, MathSciNet.  
  10. Multivariate divided differences with simple knots.
    Rabut, Christophe
    SIAM J. Numer. Anal. 38 (2000), no. 4, 1294--1311 (electronic), Math. Sci. Net.
  11. Development of block and partitioned Neville elimination  
    Alonso P.; Pena J.M.  
    Comptes Rendus de l'Academie des Sciences Series I Mathematics, 15 December 1999, vol. 329, no. 12, pp. 1091-1096(6), Ingenta.
  12. Vector Rational Interpolation Algorithms of Bulirsch-Stoer-Neville form  
    Winston L. Sweatman  
    Proceedings: Mathematical, Physical and Engineering Sciences, Vol. 454, No. 1975. (Jul. 8, 1998), pp. 1923-1932, Jstor.  
  13. 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, MathSciNet.  
  14. A Unified Approach to Evaluation Algorithms for Multivariate Polynomials  
    Suresh K. Lodha; Ron Goldman  
    Mathematics of Computation, Vol. 66, No. 220. (Oct., 1997), pp. 1521-1553, Jstor.  
  15. Backward error analysis of Neville elimination  
    Alonso P.; Gasca M.; Pe n a J.M.  
    Applied Numerical Mathematics, March 1997, vol. 23, no. 2, pp. 193-204(12), Ingenta.  
  16. Consecutive-column and -row properties of matrices and the Loewner-Neville factorization
    Fiedler, Miroslav; Markham, Thomas L.
    Linear Algebra and Its Applications, v 266, n 1-3, Nov 15, 1997, p 243-259, Compendex.  
  17. Neville elimination and approximation theory.
    Gasca, M.; Peña, J. M.
    Approximation theory, wavelets and applications (Maratea, 1994), 131--151, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 454, Kluwer Acad. Publ., Dordrecht, 1995, MathSciNet.  
  18. A matricial description of Neville elimination with applications to total positivity   
    Gasca, M.; Peña, J. M.
    Linear Algebra Appl.  202  (1994), 33--53, MathSciNet.  
  19. On a characterization of polynomials by divided differences.
    Schwaiger, J.
    Aequationes mathematicae, 1994, vol. 48, no. 2/3, pp. 317, Ingenta.   
  20. Scaled pivoting in Gauss and Neville elimination for totally positive systems  
    Gasca, M.; Peña, J. M.
    Appl. Numer. Math.  13  (1993),  no. 5, 345--355, MathSciNet.  
  21. Calculation of a differentiating matrix for equidistant nodes using Aitken's scheme. (Russian)
    Chirikalov, V. A.
    Vychisl. Prikl. Mat. (Kiev) No. 68 (1989), 22--26, 148; translation in J. Math. Sci. 69 (1994), no. 6, 1385--1388, MathSciNet.  
  22. Multivariate Divided Differences I: Basic Properties  
    M. Neamtu  
    SIAM Journal on Numerical Analysis, Vol. 29, No. 5. (Oct., 1992), pp. 1435-1445, Jstor.  
  23. The Neville-Aitken formula for rational interpolants with prescribed poles.
    Carstensen, C.; Mühlbach, G.
    Extrapolation and rational approximation (Puerto de la Cruz, 1992). Numer. Algorithms 3 (1992), no. 1-4, 133--141, MathSciNet.  
  24. Multivariate polynomial interpolation under projectivities. II. Neville-Aitken formulas.
    Gasca, M.; Mühlbach, G.
    Numer. Algorithms 2 (1992), no. 3-4, 255--277, MathSciNet.  
  25. Inherent errors in aitken's method of interpolation.
    Qaisrani, A. U.; Khan, G. M.; Khan, M. Y.
    Journal of natural sciences and mathematics, 1992, vol. 32, no. 1, pp. 63, Ingenta.   
  26. 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.
  27. Systolic design for the Aitken extrapolation formula  
    Evans, D.J.   
    Parallel Computing, v 11, n 3, Aug 28, 1989, p 385-388, Compendex.  
  28. On Aitken-Neville formulae for multivariate interpolation  
    Gasca, M.; Lebrón, E.
    Numerical approximation of partial differential equations (Madrid, 1985),  133--140, North-Holland Math. Stud., 133, North-Holland, Amsterdam, 1987, MathSciNet.  
  29. Modified Neville Iterative Inverse Interpolation Algorithm.
    Muller, Robert E. Jr.  
    Paper - American Society of Agricultural Engineers, 1986, 86-5034, 14p, Compendex.
  30. Accuracy Of Neville Extrapolants For The Eigenvalues Obtained By Finite-Difference Methods.
    Goto, Fumiaki; Bolton, Herbert Cairns  
    Technology Reports of the Iwate University, v 20, 1986, p 1-15, Compendex.
  31. Polynomial Interpolation: Lagrange versus Newton  
    Wilhelm Werner  
    Mathematics of Computation, Vol. 43, No. 167. (Jul., 1984), pp. 205-217, Jstor.  
  32. 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.  
  33. 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.  
  34. Neville type extrapolation scheme for a special expansion  
    Wu, Wen Da  
    BIT  21  (1981), no. 1, 131--135. 65B05, MathSciNet.  
  35. The Mühlbach-Neville-Aitken algorithm and some extensions.
    Brezinski, C.
    BIT 20 (1980), no. 4, 444--451, MathSciNet.  
  36. Generalized nonlinear Taylor-Cauchy-Aitken formula. (Russian)  
    Demkiv, I. I.; Susol, I. T.
    Vestnik L'vov. Politekhn. Inst. No. 141 Differentsialnye Uravneniya i ikh Prilozhen. (1980), 28--30, 114, MathSciNet.  
  37. Recurrence Relations for Computing with Modified Divided Differences  
    Fred T. Krogh  
    Mathematics of Computation, Vol. 33, No. 148. (Oct., 1979), pp. 1265-1271, Jstor.  
  38. Generalized Neville Type Extrapolation Schemes.
    Havie, T.   
    BIT (Copenhagen), v 19, n 2, 1979, p 204-213, Compendex.
  39. The general Neville-Aitken-algorithm and some applications.
    Mühlbach, G.
    Numer. Math. 31 (1978/79), no. 1, 97--110, MathSciNet.  
  40. Neville-Aitken algorithms for interpolation by functions of Cebysev-systems in the sense of Newton and in a generalized sense of Hermite.
    Mühlbach, G.
    Theory of approximation, with applications (Proc. Conf., Univ. Calgary, Calgary, Alta., 1975; dedicated to the memory of Eckard Schmidt), pp. 180--199. Academic Press, New York, 1976, MathSciNet.
  41. Block modifications of the Aitken-Steffensen method with successive approximation of the inverse operator. (Russian)  
    Volokitin, S. S.
    Differential and integral equations, No. 2 (Russian),  pp. 271--280, 316. Irkutsk. Gos. Univ., Irkutsk, 1973, MathSciNet.  
  42. Eine Verallgemeinerung von Newton-Interpolation und Neville-Aitken-Algorithmus und deren Anwendung auf die Richardson-Extrapolation. (German)
    Engels, H.
    Computing (Arch. Elektron. Rechnen) 10 (1972), 375--389, MathSciNet.  
  43. Efficient Algorithms for Polynomial Interpolation and Numerical Differentiation  
    Fred T. Krogh  
    Mathematics of Computation, Vol. 24, No. 109. (Jan., 1970), pp. 185-190, Jstor.  
  44. Note on a comparison of evaluation schemes for the interpolating polynomial
    L. B. Winrich
    The Computer Journal, Volume 12, Issue 2, (1969) pp. 154-155.
  45. Neville's method for trigonometric interpolation.
    Hunter, D. B.
    Comput. J. 11 1968/1969 311--313, MathSciNet.  
  46. 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.  
  47. A Bivariate Generalization of Hermite's Interpolation Formula  
    A. C. Ahlin  
    Mathematics of Computation, Vol. 18, No. 86. (Apr., 1964), pp. 264-273, Jstor.  
  48. Aitken-Hermite interpolation.
    Gershinsky, Morris; Levine, David A.
    J. Assoc. Comput. Mach. 11 1964 352--356, MathSciNet.  
  49. The extrapolated modified Aitken iteration method for solving elliptic difference equations   
    Evans, D. J.
    Comput. J.  6  1963/1964 193--201, MathSciNet.  
  50. Alogithm 70: interpolation by Aitken  
    Charles J. Mifsud
    Communications of the ACM, Volume 4 ,  Issue 11  (November 1961), Page: 497  
  51. 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.  
  52. On an array of Aitken   
    Moser, Leo; Wyman, Max  
    Trans. Roy. Soc. Canada. Sect. III. (3)  48,  (1954). 31--37, MathSciNet.  
  53. Some Applications of Aitken's Method of Interpolation (in Classroom Notes)  
    L. A. Aroian  
    The American Mathematical Monthly, Vol. 55, No. 9. (Nov., 1948), pp. 569-572, Jstor.  
  54. Solution of Equations by Interpolation  
    W. M. Kincaid  
    The Annals of Mathematical Statistics, Vol. 19, No. 2. (Jun., 1948), pp. 207-219, Jstor.  
  55. A modified Aitken pivotal condensation method for partial regression and multiple correlation   
    Van Boven, Alice
    Psychometrika  12,  (1947). 127--133, MathSciNet.  
  56. Aitken's method of interpolation.
    Feller, Willy On A. C.
    Quart. Appl. Math. 1, (1943) 86--87, MathSciNet.  
  57. Notes on interpolation. Part 2.  IV. Aitken's new method of inverse interpolation.  
    Lidstone, G. J.
    J. Inst. Actuar. 71, (1941). 68--95, MathSciNet.  
  58. Iterative Interpolation  
    Eric Harold Neville  
    Indian Math. Soc., Jn., v. 20, 1933, p. 87-120.  
  59. On interpolation by iteration of proportional parts, without the use of differences  
    A. C. Aitken  
    Edinburgh Math. Soc., Proc., ser. 2, v. 3, 1932, p. 56-76.  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2005