Bibliography

for

The Bisection Method

Return to Numerical Methods - Numerical Analysis

 

  1. Bisection algorithm for computing the frequency response gain of sampled-data systems---infinite-dimensional congruent transformation approach.  
    Ito, Yoshimichi; Hagiwara, Tomomichi; Maeda, Hajime; Araki, Mituhiko  
    IEEE Trans. Automat. Control 46 (2001), no. 3, 369--381, Math. Sci. Net.  
  2. n-variable bisection.  
    Münnich, Ákos;  Maksa, Gyula;  Mokken, Robert J.  
    J. Math. Psych. 44 (2000), no. 4, 569--581, Math. Sci. Net.  
  3. Bisection search algorithm for optimizing over the efficient set.  
    Thai Quynh Phong; Hoang Quang Tuyen  
    Vietnam J. Math. 28 (2000), no. 3, 217--226, Math. Sci. Net.  
  4. A .699-approximation algorithm for Max-Bisection.  
    Ye, Yinyu  
    Math. Program. 90 (2001), no. 1, Ser. A, 101--111, Math. Sci. Net.  
  5. Bisection acceleration for the symmetric tridiagonal eigenvalue problem.  
    Pan, Victor Y.; Linzer, Elliot  
    Numer. Algorithms 22 (1999), no. 1, 13--39, Math. Sci. Net.  
  6. How good is recursive bisection?  
    Simon, Horst D.;  Teng, Shang-Hua  
    SIAM J. Sci. Comput. 18 (1997), no. 5, 1436--1445, Math. Sci. Net.  
  7. Improved approximation algorithms for MAX k-CUT and MAX BISECTION.  
    Frieze, A.; Jerrum, M.  
    Algorithmica 18 (1997), no. 1, 67--81, Math. Sci. Net.  
  8. Bottleneck Resource Allocation in Manufacturing  
    Anantaram Balakrishnan, Richard L. Francis, Stephen J. Grotzinger  
    Management Science, Vol. 42, No. 11. (Nov., 1996), pp. 1611-1625, Jstor.  
  9. On 2D bisection method for double eigenvalue problems (English. English summary)  
    Ji, Xingzhi  
    J. Comput. Phys. 126 (1996), no. 1, 91--98, Math. Sci. Net.  
  10. 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.  
  11. Error analysis of a bisection method for two-objective programming. (Chinese)  
    Kong, Xiang Xu; Xu, Jing Fan; Liu, Guo Shan  
    Qufu Shifan Daxue Xuebao Ziran Kexue Ban 21 (1995), no. 5, 112--113, Math. Sci. Net.  
  12. On Enclosing Simple Roots of Nonlinear Equations  
    G. Alefeld, F. A. Potra, Yixun Shi  
    Mathematics of Computation, Vol. 61, No. 204. (Oct, 1993), pp. 733-744, Jstor.  
  13. A bisection method to find all solutions of a system of nonlinear equations  
    Mejzlík, Petr  
    Domain decomposition methods in scientific and engineering computing (University Park, PA, 1993), 277--282, Contemp. Math, 180, Amer. Math, Math. Sci. Net.  
  14. The bisection method in higher dimensions  
    Wood, G. R.  
    Math. Programming 55 (1992), no. 3, Ser. A, 319--337, Math. Sci. Net.  
  15. A family of Hermite interpolants by bisection algorithms.  
    Merrien, J.-L.  
    Numer. Algorithms 2 (1992), no. 2, 187--200, Math. Sci. Net.  
  16. Locating three-dimensional roots by a bisection method.  
    Greene, John M.  
    J. Comput. Phys. 98 (1992), no. 2, 194--198, Math. Sci. Net.  
  17. Calculation of shocked one-dimensional flows by the bisection method  
    Wu, Xiong Hua  
    Proceedings of International Conference on Scientific Computation (Hangzhou, 1991), 236--240, Ser. Appl. Math., 1, World Sci. Publishing, River Edge, NJ, 1992, Math. Sci. Net.  
  18. A parallelized algorithm for the all-row preconditioned interval Newton/generalized bisection method  
    Hu, Chen-Yi; Bayoumi, M.; Kearfott, Baker; Yang, Qing  
    Parallel processing for scientific computing (Houston, TX, 1991), 205--209, SIAM, Philadelphia, PA, (1992), Math. Sci. Net.  
  19. The incorrectness of the bisection algorithm.  
    Weyhrauch, Richard  
    Artificial intelligence and mathematical theory of computation, 467--468, Academic Press, Boston, MA, 1991, Math. Sci. Net.  
  20. Multidimensional bisection applied to global optimisation.  
    Wood, G. R.  
    Comput. Math. Appl. 21 (1991), no. 6-7, 161--172, Math. Sci. Net.  
  21. Asymptotic near optimality of the bisection method.  
    Sikorski, K.;  Trojan, G. M.  
    Numer. Math. 57 (1990), no. 5, 421--433, Math. Sci. Net.  
  22. Errata, addenda: The Bisection Method: Which Root? (in Notes)  
    Arthur Benjamin  
    American Mathematical Monthly, Vol. 97, No. 5. (May, 1990), p. 412, Jstor.  
  23. Bisection is not optimal on the average.  
    Graf, Siegfried;  Novak, Erich;  Papageorgiou, Anargyros  
    Numer. Math. 55 (1989), no. 4, 481--491, Math. Sci. Net.  
  24. A note on the bisection method (Chinese)  
    Wang, Neng Chao  
    J. Huazhong Univ. Sci. Tech. 16 (1988), no. 5, 153--155, Math. Sci. Net.  
  25. The Bisection Method: Which Root? (in Notes)  
    Arthur Benjamin  
    American Mathematical Monthly, Vol. 94, No. 9. (Nov, 1987), pp. 861-863, Jstor.  
  26. Abstract Generalized Bisection and a Cost Bound  
    R. Baker Kearfott  
    Mathematics of Computation, Vol. 49, No. 179. (Jul, 1987), pp. 187-202, Jstor.  
  27. Linear Convergence and the Bisection Algorithm (in Notes)  
    Edwin H. Kaufman, Jr, Terry D. Lenker  
    American Mathematical Monthly, Vol. 93, No. 1. (Jan, 1986), pp. 48-51, Jstor.  
  28. The Bisection Algorithm is Not Linearly Convergent  
    Sui-Sun Cheng and Tzon-Tzer Lu  
    College Math Journal: Volume 16, Number 1, (1985), Pages: 56-57.  
  29. The Bisection Method: A Best Case Analysis (in The Teaching of Mathematics)  
    A. Finbow  
    American Mathematical Monthly, Vol. 92, No. 4. (Apr, 1985), pp. 285-286, Jstor.  
  30. A Rapid Robust Rootfinder  
    Richard I. Shrager  
    Mathematics of Computation, Vol. 44, No. 169. (Jan., 1985), pp. 151-165, Jstor.  
  31. A bisection method for systems of nonlinear equations  
    Eiger, A.; Sikorski, K.; Stenger, F.  
    ACM Trans. Math. Software 10 (1984), no. 4, 367--377, Math. Sci. Net.  
  32. Solution of difference Stefan problems by bisection method. (Korean)  
    Kim, Jong Yun  
    Cho-su on In-min Kong-hwa-kuk Kwa-hak-w\u on T'ong-bo (1984), no. 5, 7--10, Math. Sci. Net.  
  33. Application of a New Complex Root-Finding Technique to the Dispersion Relations for Elastic Waves in a Fluid-Loaded Plate  
    Pieter S. Dubbelday  
    SIAM Journal on Applied Mathematics, Vol. 43, No. 5. (Oct, 1983), pp. 1127-1139, Jstor.  
  34. A Three-Dimensional Analogue to the Method of Bisections for Solving Nonlinear Equations  
    Krzysztof Sikorski  
    Mathematics of Computation, Vol. 33, No. 146. (Apr, 1979), pp. 722-738, Jstor.  
  35. An N-dimensional bisection method for solving systems of N equations in N unknowns  
    Stynes, Martin  
    Applicable Anal. 9 (1979), no. 4, 295--296, Math. Sci. Net.  
  36. A Proof of Convergence and an Error Bound for the Method of Bisection in R^n    
    Baker Kearfott  
    Mathematics of Computation, Vol. 32, No. 144. (Oct, 1978), pp. 1147-1153, Jstor.  
  37. Which Root Does the Bisection Algorithm Find? (in Classroom Notes in Applied Mathematics)  
    George Corliss  
    SIAM Review, Vol. 19, No. 2. (Apr, 1977), pp. 325-327, Jstor.  
  38. Safe Starting Regions for Iterative Methods  
    R. E. Moore, S. T. Jones  
    SIAM Journal on Numerical Analysis, Vol. 14, No. 6. (Dec, 1977), pp. 1051-1065, Jstor  
  39. A bisection method for the traveling salesman problem  
    Syslo, M. M.  
    Zastos. Mat. 16 (1977), no. 1, 59--62, Math. Sci. Net.  
  40. Bisection method for Monte Carlo integration  
    Okamoto, Masashi; Takahashi, Rinya  
    Math. Japon. 22 (1977), no. 3, 403--411, Math. Sci. Net.  

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2003