1. Some variant of Newton's method with third-order convergence
   Frontini M.; Sormani E.
   Applied Mathematics and Computation, 10 August 2003, vol. 140, no. 2, pp. 419-426(8), Ingenta.  
2. Dynamics of Newton's method for solving some equations
   Jeong M.; Ok Kim G.; Kim S.
   Computers and Graphics, April 2002, vol. 26, no. 2, pp. 271-279(9), Ingenta.  
3. Kepler equation and accelerated Newton method
   Palacios M.
   Journal of Computational and Applied Mathematics, 15 January 2002, vol. 138, no. 2, pp. 335-346(12), Ingenta.  
4. An acceleration of Newton's method: Super-Halley method
   Gutierrez J.M.; Hernandez M.A.
   Applied Mathematics and Computation, 25 January 2001, vol. 117, no. 2, pp. 223-239(17), Ingenta.  
5. Variable dimension Newton-Raphson method  
   Ng, S. W.; Lee, Y. S.  
   IEEE Trans. Circuits Systems I Fund. Theory Appl. 47 (2000), no. 6, 809--817, Math. Sci. Net.   
6. The theory of Newton's method
   Galantai A.
   Journal of Computational and Applied Mathematics, 1 December 2000, vol. 124, no. 1, pp. 25-44(20), Ingenta.  
7. From Square Roots to n-th Roots: Newton's Method in Disguise
   W. M. Priestley    
   College Math Journal: Volume 30, Number 5, (1999), Pages: 387-388.
8. Computing Square Roots Fast: Illustrating the Cubic Order of Convergence  
   John Mathews; Russell Howell  
   International Journal of Mathematics Education in Science and Technology, 1999, Vol. 30, No. 2, pp. 289-293.  
9. Variations on a Theme of Newton  
   Robert M. Corless  
   Mathematics Magazine: Volume 29, Number 1, (1998), Pages: 34-41.  
10. 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.  
11. A Continuous Version of Newton's Method
    Steve Hetzler
    College Math Journal: Volume 28, Number 5, (1997), Pages: 348-35.
12. An improvement of convergence in Newton's method
    Lopez S.
    Computer Methods in Applied Mechanics and Engineering, 30 June 1997, vol. 145, no. 3, pp. 323-327(5), Ingenta.  
13. Accelerated Convergence in Newton's Method (in Classroom Notes)  
    William F. Ford, James A. Pennline  
    SIAM Review, Vol. 38, No. 4. (Dec., 1996), pp. 658-659, Jstor.  
14. Newton's Method for Resolving Affected Equations  
    Chris Christenson
    College Math Journal: Volume 27, Number 5, (1996), Pages: 330-340.
15. An example of the secant method of iterative approximation in a fifteenth-century Sanskrit text  
    Plofker, Kim  
    Historia Math. 23 (1996), no. 3, 246--256, Math. Sci. Net.  
16. The Dynamics of Newton's Methos for Cubic Polynomials  
    James A. Walsh   
    College Math Journal: Volume 26, Number 1, (1995), Pages: 22-27.  
17. 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.  
18. Historical Development of the Newton-Raphson Method  
    Tjalling J. Ypma  
    SIAM Review, Vol. 37, No. 4. (Dec., 1995), pp. 531-551, Jstor.  
19. Average-Case Optimality of a Hybrid Secant-Bisection Method  
    Erich Novak, Klaus Ritter, Henryk Wozniakowski  
    Mathematics of Computation, Vol. 64, No. 212. (Oct., 1995), pp. 1517-1539, Jstor  
20. A generalized Newton-Raphson method using curvature  
    Lee, In-Won; Jung, Gil-Ho
    Comm. Numer. Methods Engrg. 11 (1995), no. 9, 757--763, Math. Sci. Net.  
21. Newton Raphson method, scaling at fractal boundaries and Mathematica   
    Bisoi, A. K.
    Math. Comput. Modelling 21 (1995), no. 10, 91--102, Math. Sci. Net.  
22. Historical Development of the Newton-Raphson Method  
    Tjalling J. Ypma  
    SIAM Review, Vol. 37, No. 4. (Dec., 1995), pp. 531-551, Jstor.  
23. Approximate Zeros of Quadratically Convergent Algorithms  
    Pengyuan Chen  
    Mathematics of Computation, Vol. 63, No. 207. (Jul., 1994), pp. 247-270, Jstor.  
24. Accelerated Convergence in Newton's Method (in Classroom Notes)  
    Jurgen Gerlach  
    SIAM Review, Vol. 36, No. 2. (Jun., 1994), pp. 272-276, Jstor.  
25. Pathological Functions for Newton's Method  
    George C. Donovan, Arnold R. Miller, Timothy J. Moreland  
    American Mathematical Monthly, Vol. 100, No. 1. (Jan., 1993), pp. 53-58, Jstor.  
26. The Secant Method and the Golden Mean (in Notes)  
    Melvin J. Maron, Robert J. Lopez  
    American Mathematical Monthly, Vol. 100, No. 7. (Aug. - Sep., 1993), pp. 676-678, Jstor.  
27. Using the Secant Method to Approximate the Roots of an Equation  
    Peter Lochiel Glidden  
    School Science and Mathematics, Vol. 93, No. 1, (1993), pp. 5-8.  
28. On the Superlinear Convergence of the Secant Method  
    Marco Vianello, Renato Zanovello  
    American Mathematical Monthly, Vol. 99, No. 8. (Oct., 1992), pp. 758-761, Jstor  
29. The Modified Newton Method in the Solution of Stiff Ordinary Differential Equations  
    Roger Alexander  
    Mathematics of Computation, Vol. 57, No. 196. (Oct., 1991), pp. 673-701, Jstor.  
30. A Gauss-Newton Method for Nonlinear Regression   
    M. N. Ediger, Food and Drug Administration  
    The Mathematica Journal, Vol. 1, No. 2, (Fall 1990), pp 42-44.   
31. On the R-Order of Newton-Like Methods for Enclosing Solutions of Nonlinear Equations  
    Andreas Frommer, Gunter Mayer  
    SIAM Journal on Numerical Analysis, Vol. 27, No. 1. (Feb., 1990), pp. 105-116, Jstor.  
32. A parabolic extension of Newton's method   
    Sheldon P. Gordon  and  Ellis R. Von Eschen  
    Int. J. Math. Educ. Sci. Technol.,Vol. 21, No. 4, (1990), pp. 519-525.
33. An Improved Newton's Method  
    John Mathews  
    The AMATYC Review, Vol. 10, No. 2, (Spring, 1989), pp. 9-14.  
34. 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.  
35. A Pointwise Quasi-Newton Method for Integral Equations  
    C. T. Kelley; J. I. Northrup  
    SIAM Journal on Numerical Analysis, Vol. 25, No. 5. (Oct., 1988), pp. 1138-1155, Jstor.  
36. Newton's nth Root Method Without Derivatives
    David A. Smith  
    College Math Journal: Volume 18, Number 5, (1987), Pages: 403-406.  
37. Complex Roots of Polynomials by Newton-Raphson Method   
    R. D. Murphy  
    Journal of Computers in Mathematics and Science Teaching, (1987),  pp. 44-45.  
38. A Nonmonotone Line Search Technique for Newton's Method  
    L. Grippo, F. Lampariello, S. Lucidi  
    SIAM Journal on Numerical Analysis, Vol. 23, No. 4. (Aug., 1986), pp. 707-716, Jstor.  
39. Newton's Method and the Jenkins-Traub Algorithm  
    R. N. Pederson  
    Proceedings of the American Mathematical Society, Vol. 97, No. 4. (Aug., 1986), pp. 687-690, Jstor.  
40. Attracting Orbits in Newton's Method  
    Mike Hurley  
    Transactions of the American Mathematical Society, Vol. 297, No. 1. (Sep., 1986), pp.143-158, Jstor.  
41. Complex Roots: The Bairstow-Hitchcock Method  
    Clark Kimberling  
    The Mathematics Teacher, Vol. 79, No. 4, (April, 1986), pp. 278-282.  
42. Pitfalls in the Use of Computers for the Newton-Raphson Method  
    D. Mackie  and  T. Scott  
    The Mathematical Gazette, Vol. 69, no. 450, (Dec., 1985), pp. 252-257.  
43. Newton-Raphson in reverse  
    Davies, M.  
    Math. Student 47 (1979), no. 2-4, 149--150 (1985), Math. Sci. Net.  
44. On Halley's Iteration Method (in Notes)  
    Walter Gander  
    American Mathematical Monthly, Vol. 92, No. 2. (Feb., 1985), pp. 131-134, Jstor.  
45. An Approximate Newton Method for Coupled Nonlinear Systems  
    Tony F. Chan  
    SIAM Journal on Numerical Analysis, Vol. 22, No. 5. (Oct., 1985), pp. 904-913, Jstor.  
46. A generalization of Newton Raphson  
    MacLeod, Allan J.
    Internat. J. Math. Ed. Sci. Tech. 15 (1984), no. 1, 117--120, Math. Sci. Net.   
47. Newton's Method and Symbolic Dynamics  
    Sherman Wong  
    Proceedings of the American Mathematical Society, Vol. 91, No. 2. (Jun., 1984), pp. 245-253, Jstor.  
48. On the Convergence of some Interval-Arithmetic Modifications of Newton's Method  
    G. Alefeld  
    SIAM Journal on Numerical Analysis, Vol. 21, No. 2. (Apr., 1984), pp. 363-372, Jstor.  
49. Newton's Method, Circle Maps, and Chaotic Motion  
    Donald G. Saari, John B. Urenko  
    American Mathematical Monthly, Vol. 91, No. 1. (Jan., 1984), pp. 3-17, Jstor.  
50. Aitken Sequences and Fibonacci Numbers  
    G. M. Phillips  
    American Mathematical Monthly, Vol. 91, No. 6. (Jun. - Jul., 1984), pp. 354-357, Jstor.  
51. A Nonconverging Newton Sequence  
    Peter Petek  
    Mathematics Magazine: Volume 14, Number 1, (1983), Pages: 43-45.  
52. A New Acceleration Method for Newton's Method at Singular Points  
    C. T. Kelley, R. Suresh  
    SIAM Journal on Numerical Analysis, Vol. 20, No. 5. (Oct., 1983), pp. 1001-1009, Jstor.  
53. Convergence Rates for Newton's Method at Singular Points  
    D. W. Decker, H. B. Keller, C. T. Kelley  
    SIAM Journal on Numerical Analysis, Vol. 20, No. 2. (Apr., 1983), pp. 296-314, Jstor.  
54. Analysis of Newton's Method at Irregular Singularities  
    A. Griewank, M. R. Osborne  
    SIAM Journal on Numerical Analysis, Vol. 20, No. 4. (Aug., 1983), pp. 747-773, Jstor.  
55. Local Convergence of Difference Newton-Like Methods  
    T. J. Ypma  
    Mathematics of Computation, Vol. 41, No. 164. (Oct., 1983), pp. 527-536, Jstor.  
56. Finding a Multiple Zero by Transformations and Newton-Like Methods  
    T. J. Ypma  
    SIAM Review, Vol. 25, No. 3. (Jul., 1983), pp. 365-378, Jstor.  
57. Global Convergence of a Modified Newton Iteration for Algebraic Equations  
    Kazuo Murota  
    SIAM Journal on Numerical Analysis, Vol. 19, No. 4. (Aug., 1982), pp. 793-799, Jstor.  
58. Newton-Raphson Extended  
    Neville W. Richards  
    The Mathematical Gazette, Vol. 65, no. 434, (Dec., 1981), pp. 294-295.  
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. Optimal Partitioning of Newton's Method for Calculating Roots  
    Gunter Meinardus, G. D. Taylor  
    Mathematics of Computation, Vol. 35, No. 152. (Oct., 1980), pp. 1221-1230, Jstor.  
61. Be Careful When You Dodge Round Newton  
    F. M. Arscott  
    The Mathematical Gazette, Vol. 63, no. 425, (Oct., 1979), pp. 169-172.  
62. Inverse Iteration, Ill-Conditioned Equations and Newton's Method  
    G. Peters, J. H. Wilkinson  
    SIAM Review, Vol. 21, No. 3. (Jul., 1979), pp. 339-360, Jstor.  
63. Affine Invariant Convergence Theorems for Newton's Method and Extensions to Related Methods  
    P. Deuflhard, G. Heindl  
    SIAM Journal on Numerical Analysis, Vol. 16, No. 1. (Feb., 1979), pp. 1-10, Jstor.  
64. On Newton's Method for Singular Problems  
    G. W. Reddien  
    SIAM Journal on Numerical Analysis, Vol. 15, No. 5. (Oct., 1978), pp. 993-996, Jstor.  
65. Ideas and examples for presenting the Newton-Raphson method  
    Hart, V. G.; Howard, L. N.
    Austral. Math. Soc. Gaz. 5 (1978), no. 3, 73--89, Math. Sci. Net.   
66. Sufficient conditions for elementary Newton-Raphson convergence  
    Speck, G. P.
    New Zealand Math. Mag. 14 (1977), no. 1, 34--36, Math. Sci. Net.   
67. 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.  
68. A Stable Variant of the Secant Method for Solving Nonlinear Equations  
    W. B. Gragg, G. W. Stewart  
    SIAM Journal on Numerical Analysis, Vol. 13, No. 6. (Dec., 1976), pp. 889-903, Jstor.  
69. A Note on the Convergence of Newton's Method  
    L. B. Rall  
    SIAM Journal on Numerical Analysis, Vol. 11, No. 1. (Mar., 1974), pp. 34-36, Jstor.  
70. Cycling in the Newton-Raphson algorithm  
    Ascher, Marcia
    Internat. J. Math. Ed. Sci. Tech. 5 (1974), no. 2, 229--235, Math. Sci. Net.   
71. The Use of the Secant Method in Econometric Models  
    J. Phillip Cooper, Stanley Fischer  
    The Journal of Business, Vol. 46, No. 2. (Apr., 1973), pp. 274-277, Jstor.  
72. The Kantorovich Theorem for Newton's Method (in Classroom Notes)  
    R. A. Tapia  
    American Mathematical Monthly, Vol. 78, No. 4. (Apr., 1971), pp. 389-392, Jstor.  
73. Global Convergence of Newton-Gauss-Seidel Methods  
    Jorge J. More  
    SIAM Journal on Numerical Analysis, Vol. 8, No. 2. (Jun., 1971), pp. 325-336, Jstor.  
74. The Simultaneous Newton Improvement of a Complete Set of Approximate Factors of a Polynomial  
    A. A. Grau  
    SIAM Journal on Numerical Analysis, Vol. 8, No. 2. (Jun., 1971), pp. 425-438, Jstor.  
75. Generalized Logarithmic Error and Newton's Method for the mth Root  
    David L. Phillips  
    Mathematics of Computation, Vol. 24, No. 110. (Apr., 1970), pp. 383-389, Jstor.  
76. On Aitken' s d^2  Method (in Mathematical Notes)  
    Simeon Reich  
    American Mathematical Monthly, Vol. 77, No. 3. (Mar., 1970), pp. 283-284, Jstor.  
77. Geometrical Aspects of Newton's Method  
    Walter Jennings  
    Mathematics Magazine, Vol. 42, No. 5. (Nov., 1969), pp. 262-266, Jstor.  
78. Optimal Starting Approximations for Newton's Method  
    P. H. Sterbenz, C. T. Fike  
    Mathematics of Computation, Vol. 23, No. 106. (Apr., 1969), pp. 313-318, Jstor.  
79. A Quadratically Convergent Newton-Like Method Based Upon Gaussian Elimination  
    Kenneth M. Brown  
    SIAM Journal on Numerical Analysis, Vol. 6, No. 4. (Dec., 1969), pp. 560-569, Jstor.  
80. On the Kantorovich Hypothesis for Newton's Method  
    J. E. Dennis, Jr.  
    SIAM Journal on Numerical Analysis, Vol. 6, No. 3. (Sep., 1969), pp. 493-507, Jstor.  
81. A Modified Newton-Raphson Iteration (in Classroom Notes)  
    Walter Jennings  
    American Mathematical Monthly, Vol. 75, No. 6. (Jun. - Jul., 1968), pp. 652-654, Jstor.  
82. On Steffensen's Method  
    L. W. Johnson, D. R. Scholz  
    SIAM Journal on Numerical Analysis, Vol. 5, No. 2. (Jun., 1968), pp. 296-302, Jstor.  
83. Optimal Starting Values for the Newton-Raphson Calculation of Inverses of Certain Functions  
    D. G. Moursund, G. D. Taylor  
    SIAM Journal on Numerical Analysis, Vol. 5, No. 1. (Mar., 1968), pp. 138-150, Jstor.  
84. On Newton-Raphson Iteration (in Classroom Notes)  
    J. F. Traub  
    American Mathematical Monthly, Vol. 74, No. 8. (Oct., 1967), pp. 996-998, Jstor.  
85. Monotone Iterations for Nonlinear Equations with Application to Gauss-Seidel Methods  
    James M. Ortega, Werner C. Rheinboldt  
    SIAM Journal on Numerical Analysis, Vol. 4, No. 2. (Jun., 1967), pp. 171-190, Jstor.  
86. Newton's Method for Convex Operators in Partially Ordered Spaces  
    James S. Vandergraft  
    SIAM Journal on Numerical Analysis, Vol. 4, No. 3. (Sep., 1967), pp. 406-432, Jstor.  
87. On Newton's Method and Nonlinear Simultaneous Displacements  
    J. E. Dennis, Jr.  
    SIAM Journal on Numerical Analysis, Vol. 4, No. 1. (Mar., 1967), pp. 103-108, Jstor.  
88. A Stationary Newton Method for Nonlinear Functional Equations  
    J. E. Dennis, Jr.  
    SIAM Journal on Numerical Analysis, Vol. 4, No. 2. (Jun., 1967), pp. 222-232, Jstor.  
89. Note on Newton's Method  
    L. M. Weiner  
    Mathematics Magazine, Vol. 39, No. 3. (May, 1966), pp. 143-145, Jstor.  
90. On a Discrete Version of the Newton-Raphson Method  
    Leon Wegge  
    SIAM Journal on Numerical Analysis, Vol. 3, No. 1. (Mar., 1966), pp. 134-142, Jstor.  
91. Nonlinear Difference Equations and Gauss-Seidel Type Iterative Methods  
    James M. Ortega, Maxine L. Rockoff  
    SIAM Journal on Numerical Analysis, Vol. 3, No. 3. (Sep., 1966), pp. 497-513, Jstor.  
92. On Discretization and Differentiation of Operators with Application to Newton's Method  
    James M. Ortega, Werner C. Rheinboldt  
    SIAM Journal on Numerical Analysis, Vol. 3, No. 1. (Mar., 1966), pp. 143-156, Jstor.  
93. Convergence of the Newton-Raphson method for arbitrary polynomials  
    Lancaster, P.
    Math. Gaz. 48, (1964), 291--295, Math. Sci. Net.  
94. On the Utility of Newton's Method for Computing Complex Roots of Equations (in Technical Notes and Short Papers)  
    I. M. Longman  
    Mathematics of Computation, Vol. 14, No. 70. (Apr., 1960), pp. 187-189, Jstor.  
95. Taylor's Theorem and Newton's Method (in Classroom Notes)  
    F. D. Parker  
    American Mathematical Monthly, Vol. 66, No. 1. (Jan., 1959), p. 51, Jstor.  
96. A modified Newton-Raphson process for approximation of multiple roots of polynomials  
    Milnes, Harold Willis  
    Indust. Math. 9, (1958), no. 2, 17--26, Math. Sci. Net.  
97. Newton's Method and Multiple Roots  
    Thomas E. Mott  
    American Mathematical Monthly, Vol. 64, No. 9. (Nov., 1957), pp. 635-638, Jstor.  
98. Newton's Method for Trigonometry Students (in Classroom Notes)  
    J. P. Ballantine  
    American Mathematical Monthly, Vol. 63, No. 10. (Dec., 1956), p. 722, Jstor.  
99. Newton's Method in Banach Spaces  
    Robert G. Bartle  
    Proceedings of the American Mathematical Society, Vol. 6, No. 5. (Oct., 1955), pp. 827-831, Jstor.  
100. 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.  
101. A Type of Variation on Newton's Method  
     H. J. Hamilton  
     American Mathematical Monthly, Vol. 57, No. 8. (Oct., 1950), pp. 517-522, Jstor.  
102. 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.  
103. A Modification of Newton's Method (in Classroom Notes)  
     H. S. Wall  
     American Mathematical Monthly, Vol. 55, No. 2. (Feb., 1948), pp. 90-94, Jstor.  
104. On the Newton-Raphson method of approximation  
     Richmond, H. W.  
     Edinburgh Math. Notes 1944 (1944). no. 34, 5--8, Math. Sci. Net.  
105. New Criteria for Accuracy in Approximating Real Roots by the Newton-Raphson Method  
     Myron G. Pawley  
     National Mathematics Magazine, Vol. 15, No. 3. (Dec., 1940), pp. 111-120, Jstor.  
106. On the Graeffe Method of Solution of Equations  
     L. L. Cronvich  
     American Mathematical Monthly, Vol. 46, No. 4. (Apr., 1939), pp. 185-190. Jstor.  
107. Haley's Methods for Solving Equations  
     Harry Bateman  
     American Mathematical Monthly, Vol. 45, No. 1. (Jan., 1938), pp. 11-17, Jstor.  
108. On the Convergence of Newton's Method of Approximation (in Questions, Discussions, and Notes)  
     G. T. Coate  
     American Mathematical Monthly, Vol. 44, No. 7. (Aug. - Sep., 1937), pp. 464-466, Jstor.  
109. 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.  
110. 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.  
111. On Newton's Method of Approximation  
     Henry B. Fine  
     Proceedings of the National Academy of Sciences of the United States of America, Vol. 2, No. 9. (Sep. 15, 1916), pp. 546-552, Jstor.  
112. Newton's Method in General Analysis  
     Albert A. Bennett  
     Proceedings of the National Academy of Sciences of the United States of America, Vol. 2, No. 10. (Oct. 15, 1916), pp. 592-598, Jstor.  
113. Historical Note on the Newton-Raphson Method of Approximation  
     Florian Cajori  
     American Mathematical Monthly, Vol. 18, No. 2. (Feb., 1911), pp. 29-32, Jstor.  
114. On Newton's Method of Approximation (in Notes)  
     F. Franklin  
     American Journal of Mathematics, Vol. 4, No. 1/4. (1881), pp. 275-276, Jstor.  
115. On Sir Isaac Newton's Method of Finding the Limits of the Roots of Equations. [Abstract]  
     Herbert Panmure Ribton  
     Abstracts of the Papers Communicated to the Royal Society of London, Vol. 5. (1843 - 1850), p. 630, Jstor.  

(c) John H. Mathews 2004