Bibliography for Halley's Method

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  1. Julia sets for the super-Newton method, Cauchy's method, and Halley's method.    
    Kneisl, Kyle    
    Chaos 11 (2001), no. 2, 359--370, MathSciNet.
  2. An acceleration of Newton's method: Super-Halley method
    Gutiérrez, J. M.; Hernández, M. A.
    Appl. Math. Comput. 117 (2001), no. 2-3, 223--239, MathSciNet.
  3. Halley's method: perhaps the most "rediscovered" method in the world. (Spanish)
    Ezquerro, José A.; Gutiérrez, José M.; Hernández, Miguel A.; Salanova, M. Amparo
    Margarita mathematica, 205--220, Univ. La Rioja, Logroño, 2001, MathSciNet.
  4. Convergence of Newton's and Halley's methods in the complex plane  
    Yao, Qingchuan    
    Internat. J. Math. Ed. Sci. Tech., Vol. 31, (2000), No. 6, pp. 922-925, MathSciNet.
  5. Computing Square Roots Fast: Illustrating the Cubic Order of Convergence  
    Russ Howell, John Mathews  
    Internat. J. Math. Ed. Sci. Tech., Vol. 30, (1999),  No. 2, pp. 289-293, MathSciNet.
  6. On Halley iteration.
    Yao, Q.
    Numerische mathematik, 1999, vol. 81, no. 4, pp. 647, Ingenta.  
  7. The Newton and Halley Methods for Complex Roots  
    Lily Yau and Adi Ben-Israel  
    American Mathematical Monthly, Vol. 105, No. 9, (November, 1998), pp. 806-818, Jstor.  
  8. Recurrence Relations for the Super-Halley Method.
    Gutiérrez, J. M.; Hernández, M. A.  
    Comput. Math. Appl. 36 (1998), no. 7, 1--8, MathSciNet.
  9. The super-Halley method and partial differential equations. (Spanish)    
    Ezquerro, J. A.; Gutiérrez, J. M.; Hernández, M. A.; Salanova, M. A.    
    XV Congress on Differential Equations and Applications/V Congress on Applied Mathematics, Vol. I, II (Spanish)
    (Vigo, 1997), 713--718, Colecc. Congr., 9, Univ. Vigo, Vigo, 1998, MathSciNet.
  10. The super-Halley method using divided differences.    
    Argyros, I. K.    
    Appl. Math. Lett. 10 (1997), no. 4, 91--95, MathSciNet.
  11. Geometry and convergence of Euler's and Halley's methods.  
    Melman, A.
    SIAM Rev. 39 (1997), no. 4, 728--735, MathSciNet.
  12. Halley's method and Schwarzian derivatives.   
    Palmore, Julian  
    Appl. Anal. 61 (1996), no. 1-2, 111--114, MathSciNet.
  13. On the Geometry of Halley's Method  
    T. R. Scavo, J. B. Thoo  
    American Mathematical Monthly, Vol. 102, No. 5. (May, 1995), pp. 417-426, Jstor.  
  14. Halley-like asynchronous methods for polynomial roots.    
    Trajkovic, M.; Triv ckovic, S.; Petkovic, M.    
    Conference "Filomat '94" (Ni s, 1994). Filomat No. 9, part 2 (1995), 261--271, MathSciNet.
  15. Accelerated Convergence in Newton's Method (in Classroom Notes)  
    Jurgen Gerlach  
    SIAM Review, Vol. 36, No. 2. (Jun., 1994), pp. 272-276, Jstor.  
  16. Approximate Zeros of Quadratically Convergent Algorithms  
    Pengyuan Chen  
    Mathematics of Computation, Vol. 63, No. 207. (Jul., 1994), pp. 247-270, Jstor.  
  17. On the convergence of the Halley method for nonlinear equation of one variable.    
    Chen, Dong    
    Tamkang J. Math. 24 (1993), no. 4, 461--467, MathSciNet.
  18. A Halley-like hybrid method for solving polynomial equations.
    Petkovi'c, M. S.; Mitrovi'c, Z.
    Z. Angew. Math. Mech. 72 (1992), no. 9, 447--450, MathSciNet.
  19. A note on Halley's method.   
    Verón, Miguel A. Hernández
    Numer. Math. 59 (1991), no. 3, 273--276, MathSciNet.
  20. A note on Halley's method.
    Reeves, Ray
    Computers & graphics, 1991, vol. 15, no. 1, pp. 89, Ingenta.  
  21. Recurrence relations for rational cubic methods: I. The Halley method.   
    Candela, V.; Marquina, A.
    Computing 44 (1990), no. 2, 169--184, MathSciNet.
  22. On Halley-Like Algorithms for Simultaneous Approximation of Polynomial Complex Zeros  
    Miodrag S. Petkovic  
    SIAM Journal on Numerical Analysis, Vol. 26, No. 3. (Jun., 1989), pp. 740-763, Jstor.  
  23. On the Use of Iteration Methods for Approximating the Natural Logarithm (in The Teaching of Mathematics)  
    James F. Epperson  
    American Mathematical Monthly, Vol. 96, No. 9. (Nov., 1989), pp. 831-835, Jstor.  
  24. A note on chaos and Halley's method.   
    Pickover, Clifford A.
    Comm. ACM 31 (1988), no. 11, 1326--1329, MathSciNet.
  25. On some parallel higher-order methods of Halley's type for finding multiple polynomial zeros.
    Petkovi'c, M. S.; Stefanovi'c, L. V.
    Numerical methods and approximation theory, III (Ni\v s, 1987), 329--337, Univ. Nis, Nis, 1988, MathSciNet.
  26. On Halley's Iteration Method (in Notes)  
    Walter Gander  
    American Mathematical Monthly, Vol. 92, No. 2. (Feb., 1985), pp. 131-134, Jstor.  
  27. Computational implementation of the multivariate Halley method for solving nonlinear systems of equations.
    Cuyt, Annie A. M.; Rall, L. B.
    ACM Transactions on Mathematical Software v. 11 (Mar. '85), no. 1, 20--36, MathSciNet.
  28. Numerical Stability of the Halley-Iteration for the Solution of a System of Nonlinear Equations  
    Annie A. M. Cuyt  
    Mathematics of Computation, Vol. 38, No. 157. (Jan., 1982), pp. 171-179, Jstor.  
  29. On the Convergence of Halley's Method (in Classroom Notes)  
    G. Alefeld  
    American Mathematical Monthly, Vol. 88, No. 7. (Aug. - Sep., 1981), pp. 530-536, Jstor.  
  30. On Halley's Variation of Newton's Method (in Classroom Notes)  
    George H. Brown, Jr.  
    American Mathematical Monthly, Vol. 84, No. 9. (Nov., 1977), pp. 726-728, Jstor.  
  31. On the global convergence of Halley's iteration formula.
    Davies, M.; Dawson, B.
    Numer. Math. 24 (1975), no. 2, 133--135, MathSciNet.
  32. On Newton-Raphson Iteration (in Classroom Notes)  
    J. F. Traub  
    American Mathematical Monthly, Vol. 74, No. 8. (Oct., 1967), pp. 996-998, Jstor.  
  33. An Averaging Method of Extracting Roots (in Classroom Notes)  
    J. P. Ballantine  
    American Mathematical Monthly, Vol. 63, No. 4. (Apr., 1956), pp. 249-252, Jstor.  
  34. One More Correction Formula (in Classroom Notes)  
    Ralph W. Snyder  
    American Mathematical Monthly, Vol. 62, No. 10. (Dec., 1955), pp. 722-725, Jstor.  
  35. The Solution of Equations by Continued Fractions  
    J. S. Frame  
    American Mathematical Monthly, Vol. 60, No. 5. (May, 1953), pp. 293-305, Jstor.  
  36. Another Variation of Newton's Method (in Classroom Notes)  
    J. K. Stewart  
    American Mathematical Monthly, Vol. 58, No. 5. (May, 1951), pp. 331-334, Jstor.  
  37. A Type of Variation on Newton's Method  
    H. J. Hamilton  
    American Mathematical Monthly, Vol. 57, No. 8. (Oct., 1950), pp. 517-522. Jstor.  
  38. Haley's Methods for Solving Equations  
    Harry Bateman  
    American Mathematical Monthly, Vol. 45, No. 1. (Jan., 1938), pp. 11-17, Jstor.  

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2003