Bibliography for Graeffe's Method

short

 

  1. On zeros of polynomial and vector solutions of associated polynomial system from Vieta theorem.  
    Wu, Xinyuan
    Appl. Numer. Math.  44  (2003),  no. 3, 415--423, MathSciNet.  
  2. Jacobi-Free and Complex-Free Method for Finding Simultaneously All Zeros of Polynomials Having only Real Zeros
    Wu, Xingyuan; Shao, Rong; Yiran, Z.H.U.  
    Computers and Mathematics with Applications, v 46, n 8-9, October/November, 2003, p 1387-1395, Compendex.  
  3. On the Geometry of Graeffe Iteration
    Malajovich, G.; Zubelli, J. P.
    Journal of Complexity, 2001, vol. 17, no. 3, pp. 541-573, Ingenta.
  4. Iterative methods for roots of polynomials  
    Mekwi, W.R.
    Masters thesis,  (2001), University of Oxford, U. K.
  5. A generalized Graeffe's iteration for evaluating polynomials and rational functions  
    Gemignani, Luca  
    Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC, 2001, p 143-149, Compendex.
  6. Tangent Graeffe Iteration  
    Malajovich, G. and Zubelli, J. P.
    Cornell University Library, MSRI 1999-047, 27 Aug 1999
  7. Fast parallel algorithms for Graeffe's root squaring technique
    Jana, P.K.; Sinha, B.P.
    Computers & Mathematics with Applications, v 35, n 3, Feb, 1998, p 71-80, Compendex.
  8. Solving Polynomials with Computers
    Victor Y. Pan  
    American Scientist, 86, 62-69, (January-February 1998).
  9. Solving a Polynomial Equation: Some History and Recent Progress  
    Victor Y. Pan  
    SIAM Review, Vol. 39, No. 2. (Jun., 1997), pp. 187-220, Jstor.
  10. Graeffe's, Chebyshev-like, and Cardinal's processes for splitting a polynomial into factors.    
    Bini, Dario; Pan, Victor Y.    
    Special issue for the Foundations of Computational Mathematics Conference (Rio de Janeiro, 1997). J. Complexity 12 (1996), no. 4, 492--511, MathSciNet.  
  11. A note on the computation of double zeroes of polynomials via Vieta's equations.  
    Hoy, Annegret
    Wiss. Z. Martin-Luther-Univ. Halle-Wittenberg Math.-Natur. Reihe  40  (1991),  no. 3, 143--146, MathSciNet.  
  12. A highly parallel algorithm for root extraction  
    L.H. Jamieson and T.A. Rice  
    IEEE Trans. Comput. 38 (1989) 443--449.
  13. Root squaring using level-index arithmetic  
    C.W. Clenshaw and P.R. Turner  
    Computing 43 (1989) 171--185.
  14. Reciprocal Polynomials Having Small Measure  
    David W. Boyd
    Mathematics of Computation, Vol. 35, No. 152. (Oct., 1980), pp. 1361-1377, Jstor.  
  15. An Exact Method for Finding the Roots of a Complex Polynomial
    James R. Pinkert       
    ACM Transactions on Mathematical Software (TOMS), Volume 2 ,  Issue 4  (December 1976), pp. 351 - 363.
  16. Algorithm 340: roots of polynomials by a root-squaring and resultant routine  
    Albert Noltemeier     
    Communications of the ACM, Volume 11 ,  Issue 11  (November 1968), pp. 779 - 782.
  17. Graeffe's method for eigenvalues.
    Pólya, G.
    Numer. Math. 11 1968, 315--319, MathSciNet.  
  18. Remark on algorithm 256: modified Graeffe method  
    G. Stern
    Communications of the ACM, Volume 9 ,  Issue 9  (September 1966), p. 687  
  19. Modified Graeffe method (Algorithm 256)  
    A. A. Grau  
    Comm. ACM 8 (1965) 379--380.
  20. Finding zeros of a polynomial by the Q-D algorithm  
    P. Henrici and Bruce O. Watkins
    Communications of the ACM, Volume 8 ,  Issue 9  (September 1965), 570 - 574.  
  21. The Complete Root-Squaring Method  
    D. H. Lehmer  
    Journal of the Society for Industrial and Applied Mathematics, Vol. 11, No. 3. (Sep., 1963), pp. 705-717, Jstor.  
  22. On the Reduction of Number Range in the Use of the Graeffe Process   
    A. A. Grau  
    J. Assoc. Comput. Mach. 10 (1963) 538--544.
  23. On a modification of the QD-algorithm with Graeffe-type convergence.    
    Rutishauser, Heinz    
    Z. Angew. Math. Phys. 13 1962 493--496.
  24. Resultant Procedure and the Mechanization of the Graeffe Process      
    Bareiss, Erwin H.    
    J. Assoc. Comput. Mach. 7 1960 346--386.
  25. Truncation Error in the Graeffe Root-Squaring Method  
    Weeg, Gerard P.    
    J. Assoc. Comput. Mach. 7  (1960) 69--71.
  26. Dandelin, Lobacevskii, or Graeffe  
    Alston S. Householder  
    The American Mathematical Monthly, Vol. 66, No. 6. (Jun. - Jul., 1959), pp. 464-466, Jstor.  
  27. On modern matrix iteration processes of Bernoulli and Graeffe type.
    Bauer, F. L.
    J. Assoc. Comput. Mach. 5 1958 246--257, MathSciNet.  
  28. Notes on the Graeffe Method of Root Squaring (in Mathematical Notes)  
    G. C. Best  
    American Mathematical Monthly, Vol. 56, No. 2. (Feb., 1949), pp. 91-94, Jstor.  
  29. The Determination of the Complex Zeros of A Polynomial  
    G. C. Best
    The American Mathematical Monthly, Vol. 54, No. 5. (May, 1947), pp. 269-273, Jstor.  
  30. The accuracy of the root-squaring method for solving equations  
    P.G. Hoel and D.D. Wall  
    J. Math. and Phys. 26 (1947) 156--164.
  31. The Graeffe Process  
    K. Mitchell  
    Math. Tab. Aids Comp. 2 (1946/47) 57--59.
  32. On Graeffe's method for solving algebraic equations.   
    Bodewig, E.
    Quart. Appl. Math. 4, (1946). 177--190, MathSciNet.  
  33. Observations on a theorem of Rey Pastor on Graeffe's method. (Spanish)   
    Vigil, Luis
    Publ. Inst. Mat. Univ. Nac. Litoral 6, (1946). 191--193, MathSciNet.  
  34. The Graeffe Process as Applied to Power Series  
    Lehmer, D. H.
    Mathematical Tables and Other Aids to Computation, Vol. 1, No. 10. (Apr., 1945), pp. 377-383, Jstor.  
  35. The method of Graeffe for solving algebraic equations. (Spanish)
    Massera, Jose L.
    Bol. Fac. Ingen. Montevideo 3, (1945). (Ano 10), 1--20.
  36. On the transformation of the method of Graeffe. (Spanish)
    Babini, J.
    Publ. Inst. Mat. Univ. Nac. Litoral 5, (1945). 45--49, MathSciNet.  
  37. On the Graeffe Method of Solution of Equations  
    L. L. Cronvich  
    American Mathematical Monthly, Vol. 46, No. 4. (Apr., 1939), pp. 185-190. Jstor.  
  38. Graeffe's Method and Complex Roots (in Questions, Discussions, and Notes)  
    B. A. Hausmann  
    American Mathematical Monthly, Vol. 43, No. 4. (Apr., 1936), pp. 225-229. Jstor.  
  39. On Graeffe's Method for the Numerical Solution of Algebraic Equations  
    C. A. Hutchinson  
    American Mathematical Monthly, Vol. 42, No. 3. (Mar., 1935), pp. 149-161, Jstor.  
  40. Note on solving algebraic equations by root cubing
    A.C. Aitken
    Math. Gaz. 15 (1931) 490--491.
  41. The Cubic and Biquadratic Equations Vieta's Transformation in the Complex Plane  
    Archibald Henderson; A. W. Hobbs  
    The American Mathematical Monthly, Vol. 37, No. 10. (Dec., 1930), pp. 515-521, Jstor.  
  42. On Graeffe's method for complex roots of algebraic equations  
    S. Brodetsky and G. Smeal  
    Proc. Cambridge Philos. Soc. 22 (1924) 83--87.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2005