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. Directional Halley and quasi-Halley methods in n variables.
   Levin, Yuri; Ben-Israel, Adi
   Inherently parallel algorithms in feasibility and optimization and their applications (Haifa, 2000), 345--367,  Stud. Comput. Math., 8, North-Holland, Amsterdam, 2001, MathSciNet.
5. On the monotone convergence of a Chebysheff-Halley method in partially ordered topological spaces.
   Argyros, Ioannis K.
   Math. Sci. Res. Hot-Line 5 (2001), no. 1, 9--17, MathSciNet.
6. A modification of the super-Halley method under mild differentiability conditions (Letter to the Editor).
   Ezquerro, J.A.; Hernandez, M.A.
   Journal of Computational and Applied Mathematics, 2000, vol. 114, no. 2, pp. 405, Ingenta.  
7. Convergence of Newton's and Halley's methods in the complex plane  
   Yao, Qingchuan    
   Internat. J. Math. Ed. Sci. Tech. 31 (2000), no. 6, 922--925, MathSciNet.
8. Directional Halley and quasi-Halley methods in n variables. Inherently parallel algorithms in feasibility and optimization and their applications    
   Levin, Yuri; Ben-Israel, Adi    
   (Haifa, 2000), 345--367, Stud. Comput. Math., 8, North-Holland, Amsterdam, 2001, MathSciNet.
9. A modification of the super-Halley method under mild differentiability conditions.   
   Ezquerro, J. A.; Hernández, M. A.
   J. Comput. Appl. Math. 114 (2000), no. 2, 405--409, MathSciNet.
10. Error bounds for the Halley method in Banach spaces.
    Argyros, Ioannis K.; Tabatabai, Mohammad A.
    Adv. Nonlinear Var. Inequal. 3 (2000), no. 2, 1--13, MathSciNet.
11. On new properties of the Halley method. (Ukrainian)
    Podlevski, B. M.
    Dopov. Nats. Akad. Nauk Ukr. Mat. Prirodozn. Tekh. Nauki 1999, no. 12, 21--26, MathSciNet.
12. 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.
13. Computing Square Roots Fast: Illustrating the Cubic Order of Convergence  
    Russ Howell, John Mathews  
    International Journal of Mathematics Education in Science and Technology, 1999, Vol. 30, No. 2, pp. 289-293.
14. On a class of iterations containing the Chebyshev and the Halley methods.   
    Ezquerro, J. A.; Hernández, M. A.
    Publ. Math. Debrecen 54 (1999), no. 3-4, 403--415, MathSciNet.
15. Indices of convexity and concavity. Application to Halley method.  
    Hernández, M. A.; Salanova, M. A.
    Appl. Math. Comput. 103 (1999), no. 1, 27--49, MathSciNet.
16. Improved error bounds for a Chebysheff-Halley-type method.
    Argyros, I.K.
    Acta mathematica Hungarica, 1999, vol. 84, no. 3, pp. 209, Ingenta.  
17. Halley-Like Method with Corrections for the Inclusion of Polynomial Zeros.
    Petkovic, M.S.
    Computing, 1999, vol. 62, no. 1, pp. 69, Ingenta.  
18. On Halley iteration.
    Yao, Q.
    Numerische mathematik, 1999, vol. 81, no. 4, pp. 647, Ingenta.  
19. 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.  
20. Recurrence Relations for the Super-Halley Method.
    Gutiérrez, J. M.; Hernández, M. A.  
    Comput. Math. Appl. 36 (1998), no. 7, 1--8, MathSciNet.
21. Improving the order and rates of convergence for the super-Halley method in Banach spaces.  
    Argyros, Ioannis K.  
    Korean J. Comput. Appl. Math. 5 (1998), no. 2, 465--474, MathSciNet.
22. Convergence of the iteration of Halley's family and Smale operator class in Banach space.
    Wang, Xinghua
    Scientia Sinica. Series A, Mathematical, physical, astronomical & technical sciences, 1998, vol. 41, no. 7, pp. 700, Ingenta.  
23. On the convergence of Halley-like method.
    Ili'c, Snazana; Herceg, Djordje; Petkovi'c, Miodrag
    Novi Sad J. Math. 28 (1998), no. 3, 61--70, MathSciNet.
24. 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.
25. The super-Halley method using divided differences.    
    Argyros, I. K.    
    Appl. Math. Lett. 10 (1997), no. 4, 91--95, MathSciNet.
26. Geometry and convergence of Euler's and Halley's methods.  
    Melman, A.
    SIAM Rev. 39 (1997), no. 4, 728--735, MathSciNet.
27. Convergence on the iteration of Halley family in weak conditions.
    Wang, Xinghua
    Chinese Sci. Bull. 42 (1997), no. 7, 552--555, MathSciNet.
28. Convergence of iterations of the Halley family under weak conditions. (Chinese)
    Wang, Xing Hua
    Kexue Tongbao (Chinese) 42 (1997), no. 2, 119--122, MathSciNet.
29. The error estimates of Halley's method.  
    Han, Dan-fu; Wang, Xing-hua  
    Numer. Math. J. Chinese Univ. (English Ser.) 6 (1997), no. 2, 231--240, MathSciNet.
30. Halley's method and Schwarzian derivatives.   
    Palmore, Julian  
    Appl. Anal. 61 (1996), no. 1-2, 111--114, MathSciNet.
31. On the convergence of a Chebysheff-Halley--type method using divided differences of order one.
    Argyros, Ioannis K.
    Rev. Acad. Cienc. Zaragoza (2) 51 (1996), 27--45, MathSciNet.
32. 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.  
33. A note on the convergence of Halley's method for solving operator equations.    
    Zheng, Shi Ming; Robbie, Desmond    
    J. Austral. Math. Soc. Ser. B 37 (1995), no. 1, 16--25, MathSciNet.
34. Halley's Method for the Matrix Sector Function.
    Koç, Çetin Kaya; Bakkaloglu, Bertan
    IEEE Trans. Automat. Control 40 (1995), no. 5, 944--949, MathSciNet.
35. Halley's Method for the Matrix Sector Function.
    Koc, C. K.; Bakkaloglu, B.
    Materials transactions, JIM, 1995, vol. 36, no. 1, pp. 944, Ingenta.  
36. Convergence results for the super-Halley method using divided differences.  
    Argyros, Ioannis K.
    Funct. Approx. Comment. Math. 23 (1994), 109--122 (1995), MathSciNet.
37. 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.
38. Accelerated Convergence in Newton's Method (in Classroom Notes)  
    Jurgen Gerlach  
    SIAM Review, Vol. 36, No. 2. (Jun., 1994), pp. 272-276, Jstor.  
39. Approximate Zeros of Quadratically Convergent Algorithms  
    Pengyuan Chen  
    Mathematics of Computation, Vol. 63, No. 207. (Jul., 1994), pp. 247-270, Jstor.  
40. 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.
41. Ostrowski-Kantorovich theorem and S-order of convergence of Halley method in Banach spaces.
    Dong, Chen
    Commentationes mathematicae Universitatis Carolinae, 1993, vol. 34, no. 1, pp. 153, Ingenta.  
42. A Note on the Halley Method in Banach Spaces.
    Chen, Dong; Argyros, I.K.; Qian, Q.S.
    Applied mathematics and computation, 1993, vol. 58, no. 2/3, pp. 215, Ingenta.  
43. Further insights into Halley's method.
    Reeves, Ray
    Computers & graphics, 1992, vol. 16, no. 2, pp. 235, Ingenta.  
44. 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.
45. A note on Halley's method.   
    Verón, Miguel A. Hernández
    Numer. Math. 59 (1991), no. 3, 273--276, MathSciNet.
46. A note on Halley's method.
    Reeves, Ray
    Computers & graphics, 1991, vol. 15, no. 1, pp. 89, Ingenta.  
47. Point estimates for Halley's iteration. (Chinese)
    Zheng, Shi Ming
    Acta Math. Appl. Sinica 14 (1991), no. 3, 376--383, MathSciNet.
48. Recurrence relations for rational cubic methods: I. The Halley method.   
    Candela, V.; Marquina, A.
    Computing 44 (1990), no. 2, 169--184, MathSciNet.
49. 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.  
50. 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.  
51. A note on chaos and Halley's method.   
    Pickover, Clifford A.
    Comm. ACM 31 (1988), no. 11, 1326--1329, MathSciNet.
52. 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.
53. Some modifications of the parallel Halley iteration method and their convergence.    
    Wang, De Ren; Wu, Yu Jiang    
    Computing 38 (1987), no. 1, 75--87, MathSciNet.
54. On Halley's Iteration Method (in Notes)  
    Walter Gander  
    American Mathematical Monthly, Vol. 92, No. 2. (Feb., 1985), pp. 131-134, Jstor.  
55. The parallel Halley iteration method with circular arithmetic for finding all zeroes of a polynomial. (Chinese)    
    Wang, Xing Hua; Zheng, Shi Ming    
    Numer. Math. J. Chinese Univ. 7 (1985), no. 4, 308--314, MathSciNet.
56. 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.
57. A local convergence theorem for Halley's iteration method for finding complex zeros. (Chinese)
    Sun, Zhan Shan
    Numer. Math. J. Chinese Univ. 6 (1984), no. 3, 222--227, MathSciNet.
58. 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.  
59. 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.  
60. 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.  
61. On the global convergence of Halley's iteration formula.
    Davies, M.; Dawson, B.
    Numer. Math. 24 (1975), no. 2, 133--135, MathSciNet.
62. On Newton-Raphson Iteration (in Classroom Notes)  
    J. F. Traub  
    American Mathematical Monthly, Vol. 74, No. 8. (Oct., 1967), pp. 996-998, Jstor.  
63. 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.  
64. One More Correction Formula (in Classroom Notes)  
    Ralph W. Snyder  
    American Mathematical Monthly, Vol. 62, No. 10. (Dec., 1955), pp. 722-725, Jstor.  
65. The Solution of Equations by Continued Fractions  
    J. S. Frame  
    American Mathematical Monthly, Vol. 60, No. 5. (May, 1953), pp. 293-305, Jstor.  
66. 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.  
67. A Type of Variation on Newton's Method  
    H. J. Hamilton  
    American Mathematical Monthly, Vol. 57, No. 8. (Oct., 1950), pp. 517-522. Jstor.  
68. 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