Bibliography for Horner's Method

short

  1. The wonder of Horner's method
    Pathan, A.; Collyer, T.
    Mathematical Gazette, 2003, vol. 87, no. 509, pp. 230-242, Ingenta.
  2. Horner's rule for interval evaluation revisited.  
    Ceberio, M.; Granvilliers, L.
    Computing (Vienna/New York), v 69, n 1, 2002, p 51-81, MathSciNet.  
  3. On the multivariate Horner scheme. II. Running error analysis.
    Peña, J. M.; Sauer, T.
    Computing (Vienna/New York), v 65, 2000, p 313-322, Compendex.
  4. On the multivariate Horner scheme.
    Peña, J. M.; Sauer, Thomas
    SIAM J. Numer. Anal. 37 (2000), no. 4, 1186--1197 (electronic), MathSciNet.  
  5. Synthetic division based integration of rational functions of bivariate polynomial numerators with linear denominators over a unit triangle in the local parametric space.  
    Rathod, H. T.; Shajedul Karim, MD.
    Comput. Methods Appl. Mech. Engrg.  181  (2000),  no. 1-3, 191--235, MathSciNet.  
  6. Randomness of Horner's rule and a new method of generating random numbers.
    Yaguchi, Hirotake
    Monte Carlo Methods Appl. 6 (2000), no. 1, 61--76, MathSciNet.  
  7. Thomas Horner versus Holdred: an episode in the history of root computation.
    Fuller, A.
    Historia Math. 26 (1999), no. 1, 29--51, MathSciNet.  
  8. A Genuine Application of Synthetic Division, Descartes' Rule of Signs, and All That Stuff  
    Dwight D. Freund  
    The College Mathematics Journal, Vol. 26, No. 2. (Mar., 1995), pp. 106-110, Jstor.  
  9. Transformation of polynomial evaluation to a pipeline via Horner's rule.
    Harrison, Peter G.; While, R. Lyndon
    Science of Computer Programming, v 24, n 1, Feb, 1995, p 83-95, Compendex.  
  10. Efficient throughput optimization of feedback linear computations using generalized Horner's scheme  
    Rabaey, Jan M.; Potkonjak, Miodrag; Wakabayashi, Kazutoshi  
    ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings, v 4, Image and Multi-Dimensional Signal Processing, 1995, p 2659-2662, Compendex.
  11. Similarities between Chinese and Arabic mathematical writings. I. Root extraction.  
    Chemla, Karine
    Arabic Sci. Philos.  4  (1994),  no. 2, 207--266, MathSciNet.  
  12. Generalization of the Horner scheme. (Russian)
    Aleksei, S. F.
    Algebraic structures and geometry (Russian), 3--6, 156, "Shtiintsa", Kishinev, 1991, MathSciNet.  
  13. Evaluation of Multivariate Polynomials and Their Derivatives  
    J. Carnicer; M. Gasca  
    Mathematics of Computation, Vol. 54, No. 189. (Jan., 1990), pp. 231-243, Jstor.  
  14. A Fast Parallel Horner Algorithm.
    Dowling, Michael L.
    SIAM Journal on Computing, v 19, n 1, Feb, 1990, p 133-142, Compendex.  
  15. Synthetic Division, Taylor Polynomials, Partial Fractions
    Lambert, Howard
    Mathematics and computer education, 1989, vol. 23, no. 2, pp. 95 , Ingenta.
  16. Peturbation Analysis of Horner's Method for Nice Cases.
    Dunham, Charles B.
    Signum newsletter, 1989, vol. 24, no. 2/3, pp. 8, Ingenta.
  17. Horner's rule and the computation of linear recurrences.
    Gries, David; Pascoletti, Adriano; Sbriz, Luigi
    Inform. Process. Lett. 25 (1987), no. 4, 237--240, MathSciNet.  
  18. 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.  
  19. Partial Fraction Evaluation and Incomplete Decomposition of a Rational Function Whose Denominator Contains a Repeated Polynomial Factor  
    J. F. Mahoney  
    Mathematics of Computation, Vol. 44, No. 169. (Jan., 1985), pp. 167-175, Jstor.  
  20. Parallel-Serial Multiplication Using Booth's Algorithm And Horner's Scheme.
    Stoelzle, Anton; Rainer, Alois; Ulbrich, Walter  
    Proceedings - IEEE International Symposium on Circuits and Systems, 1985, p 1389-1390, Compendex.
  21. Estimation of polynomial roots by continued fractions.  
    Klán, Petr
    Kybernetika (Prague)  21  (1985),  no. 6, 457--469, MathSciNet.  
  22. Bilinear Transformation Of Multivariable Polynomials Using The Horner Method  
    Smart, Nancy M.; Barnett, Stephen
    International Journal of Control, v 37, n 4, Apr, 1983, p 861-865, Compendex.  
  23. Rounding error analysis of Horner's scheme.
    Müller, K.-H.
    Computing (Vienna/New York), v 30, n 4, 1983, p 285-303, MathSciNet.  
  24. Synthetic Division Shortened (in Classroom Capsules)   
    Warren Page; Leo Chosid  
    The Two-Year College Mathematics Journal, Vol. 12, No. 5. (Nov., 1981), pp. 334-336, Jstor.  
  25. A modification of Horner's scheme. (Russian)
    Vetoshkin, A. M.
    Zh. Vychisl. Mat. i Mat. Fiz. 21 (1981), no. 5, 1311--1312, 1359, MathSciNet.  
  26. The Chinese connection between the Pascal triangle and the solution of numerical equations of any degree.  
    Lam, Lay Yong
    Historia Math.  7  (1980), no. 4, 407--424, MathSciNet.  
  27. Differentiation and Synthetic Division (in Classroom Capsules)  
    Dan Kalman  
    The Two-Year College Mathematics Journal, Vol. 10, No. 1. (Jan., 1979), p. 37, Jstor.  
  28. Determination of zeros of polynomials by synthetic division  
    Lee, Charles C.; Niu, H. P.
    Internat. J. Comput. Math. 7 (1979), no. 2, 131--139, MathSciNet.  
  29. Applications and generalizations of Horner's algorithm. (Slovenian)
    Bohte, Zvonimir
    Obzornik Mat. Fiz. 26 (1979), no. 5, 129--140, MathSciNet.  
  30. Method Of Paralleling Horner Circuits And Its Application To Digital Computing Devices.
    P'yavchenko, O. N.; Surzhenko, I. F.; Romm, Yu. E.  
    Automatic Control and Computer Sciences (English translation of Avtomatika i Vychislitel'naya Tekhnika), v 12, n 5, 1978, p 64-68, Compendex.
  31. Generalized Horner Algorithm For Computing Integrals Involving The Matrix Exponential  
    Van Loan, Charles
    Proceedings of the IEEE Conference on Decision and Control, 1978, p 74-79, Compendex.  
  32. Polynomial Evaluation Schemes   
    A. C. R. Newbery  
    Mathematics of Computation, Vol. 29, No. 132. (Oct., 1975), pp. 1046-1050, Jstor.  
  33. Error Analysis for Polynomial Evaluation  
    A. C. R. Newbery  
    Mathematics of Computation, Vol. 28, No. 127. (Jul., 1974), pp. 789-793, Jstor.  
  34. Error Analysis of the Algorithm for Shifting the Zeros of a Polynomial by Synthetic Division  
    G. W. Stewart  
    Mathematics of Computation, Vol. 25, No. 113. (Jan., 1971), pp. 135-139, Jstor.  
  35. Horner's rule is uniquely optimal.
    Borodin, Allan
    Theory of machines and computations (Proc. Internat. Sympos., Technion, Haifa, 1971), pp. 45--58. Academic Press, New York, 1971, MathSciNet.  
  36. Nomogramme für das Horner-Schema. (German)
    Friedrich, H.
    Monatsb. Deutsch. Akad. Wiss. Berlin 11 1969 795--798, MathSciNet.  
  37. Bounds for the Horner Sums  
    Manfred Reimer  
    SIAM Journal on Numerical Analysis, Vol. 5, No. 3. (Sep., 1968), pp. 461-469, Jstor.  
  38. The Ruffini-Horner Method, §53
    Whittaker, E. T. and Robinson, G.
    The Calculus of Observations: A Treatise on Numerical Mathematics, 4th ed. New York: Dover, pp. 100-106, 1967, MathSciNet.  
  39. An application of Horner's division scheme in the solution of algebriac congruences of higher degree. (Russian)
    Lysov, A. I.
    Orsk. Gos. Ped. Inst. U\v cen. Zap. Vyp. 5 Kaf. Mat. (1963), 71--73, MathSciNet.  
  40. Digit-by-digit methods for polynomials.  
    Meggitt, J. E.
    IBM J. Res. Develop.  7  1963 237--245, MathSciNet.  
  41. Generalizations of Horner's rule for polynomial evaluation.
    Dorn, W. S.
    IBM J. Res. Develop. 6 1962 239--245, MathSciNet.  
  42. On the Synthetic Division Process (in Classroom Notes)  
    W. W. Comfort; Thomas E. Mott  
    The American Mathematical Monthly, Vol. 66, No. 8. (Oct., 1959), p. 717, Jstor.  
  43. A binary form of Horner's method  
    S. Gill
    The Computer Journal, Volume 1, Issue 2, July 1958, pp. 84-86.
  44. Horner's Method in Chinese Mathematics  
    Wang Ling and Joseph Needham  
    T'oung Pao, 1955, 43: p345-401.
  45. On two problems in abstract algebra connected with Horner's rule.  
    Ostrowski, A.
    Studies in mathematics and mechanics presented to Richard von Mises,  pp. 40--48. Academic Press Inc., New York, 1954, MathSciNet.  
  46. The evaluation of the complex roots of algebraic equations.  
    Cornock, A. F.; Hughes, Joan M.
    Philos. Mag. (7)  34,  (1943). 314--320, MathSciNet.  
  47. Discussion: A Note on Horner's Method of Solving an Algebraic Equation (in Questions and Discussions)  
    C. W. Bruce  
    The American Mathematical Monthly, Vol. 37, No. 2. (Feb., 1930), pp. 80-81, Jstor.  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004