Bibliography for the Secant Method

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  1. Associativity of the Secant Method
    Northshield, S.
    American Mathematical Monthly, 2002, vol. 109, no. 3, pp. 246-257, Ingenta.
  2. Modified Newton and secant methods for solving an order O([Graphics:../Images/SecantMethodBib_gr_1.gif]) finite-difference problem.
    Lin, Zhenghua; Yu, Xiaolin; Sheng, Zhongping
    Ann. Differential Equations 16 (2000), no. 2, 134--144, Math. Sci. Net.
  3. The application of Julia set to Newton-secants method.
    Tomova, Anna
    Applications of mathematics in engineering and economics (Sozopol, 1999), 94--95, Heron Press, Sofia, 2000, Math. Sci. Net.
  4. A new type of recurrence relations for the secant method.
    Hernández, M. A.; Rubio, M. J.
    Int. J. Comput. Math. 72 (1999), no. 4, 477--490, Math. Sci. Net.   
  5. Secant methods for semismooth equations.
    Potra, Florian A.; Qi, Liqun; Sun, Defeng
    Numer. Math. 80 (1998), no. 2, 305--324, Math. Sci. Net.   
  6. A note on inexact secant methods.
    Cuatinacs, Emil
    Rev. Anal. Numér. Théor. Approx. 25 (1996), no. 1-2, 33--41, Math. Sci. Net.  
  7. 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.  
  8. 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  
  9. 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.  
  10. 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.  
  11. On the secant method.
    Argyros, Ioannis K.
    Publ. Math. Debrecen 43 (1993), no. 3-4, 223--238, Math. Sci. Net.  
  12. Exact order of convergence of the secant method.
    Raydan, M.
    J. Optim. Theory Appl. 78 (1993), no. 3, 541--551, Math. Sci. Net.  
  13. 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  
  14. Improved Error Bounds for the Modified Secant Method.
    Argyros, I.K.
    International journal of computer mathematics, 1992, vol. 43, no. 1/2, pp. 99, Ingenta.
  15. Error bounds for the secant method.
    Argyros, Ioannis K.
    Math. Slovaca 41 (1991), no. 1, 69--82, Math. Sci. Net.  
  16. Error for the modified secant method.
    Argyros, Ioannis K.
    BIT 30 (1990), no. 1, 92--100, Math. Sci. Net.  
  17. On superlinear convergence of some stable variants of the secant method.
    Burdakov, O. P.
    Z. Angew. Math. Mech. 66 (1986), no. 12, 615--622, Math. Sci. Net.  
  18. An interval version of the secant method.
    Neumaier, A.
    BIT 24 (1984), no. 3, 366--372, Math. Sci. Net.  
  19. An error analysis for the secant method.
    Potra, Florian-A.
    Numer. Math. 38 (1981/82), no. 3, 427--445, Math. Sci. Net.
  20. On a modified secant method.
    Potra, F.-A.
    Anal. Numér. Théor. Approx. 8 (1979), no. 2, 203--214, Math. Sci. Net.
  21. Theory of multivariate secant methods.
    Jankowska, Janina
    SIAM J. Numer. Anal. 16 (1979), no. 4, 547--562, Math. Sci. Net.
  22. Three new algorithms based on the sequential secant method.
    Martínez, José Mario
    BIT 19 (1979), no. 2, 236--243, Math. Sci. Net.
  23. A secant method for multiple roots.
    King, Richard F. Nordisk Tidskr. Informationsbehandling (BIT) 17 (1977), no. 3, 321--328, Math. Sci. Net.
  24. 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.  
  25. A Globally Converging Secant Method with Applications to Boundary Value Problems
    E. Polak
    SIAM Journal on Numerical Analysis, Vol. 11, No. 3. (Jun., 1974), pp. 529-537, Jstor  
  26. A Globally Converging Secant Method with Applications to Boundary Value Problems  
    E. Polak  
    SIAM Journal on Numerical Analysis, Vol. 11, No. 3. (Jun., 1974), pp. 529-537, Jstor.  
  27. Some iterations for factoring a polynomial. II. A generalization of the secant method.
    Stewart, G. W.
    Numer. Math. 22 (1973/74), 33--36, Math. Sci. Net.
  28. 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.  
  29. On the behavior of the secant method near a multiple root.
    Espelid, T. O.
    Nordisk Tidskr. Informationsbehandling (BIT) 12 (1972), 112--115, Math. Sci. Net.
  30. An algorithm for solving non-linear equations based on the secant method.
    Barnes, J. G. P.
    Comput. J. 8 1965 66--72, Math. Sci. Net.

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2003