Bibliography for Fibonacci Search

unabridged

 

  1. On Fibonacci search method with k-Lucas numbers
    Yildiz, Bunyamin; Karaduman, Erdal
    Applied Mathematics and Computation (New York), v 143, n 2-3, Nov 10, 2003, p 523-531, Compendex.
  2. Single Variable Optimization When Calculus Fails: Fibonacci Search Methods in Nonlinear Optimization Using MAPLE
    Fox
    Computers in Education Journal, 2002, vol. 12, no. 2, pp. 64-71, Ingenta.
  3. Can Fibonacci numbers improve your search algorithms?
    Schweber, Bill  
    EDN v. 45 no20 (i.e. 21) (Oct. 12 2000) p. 65-68, FirstSearch.  
  4. An evolutionary strategy for minimizing unimodal functions. (Chinese)    
    Wang, Yun Cheng; Tang, Huan Wen    
    Math. Numer. Sin. 22 (2000), no. 4, 465--472, MathSciNet.  
  5. New Fibonacci and Lucas primes.
    Dubner, Harvey; Keller, Wilfrid
    Math. Comp. 68 (1999), no. 225, 417--427, S1--S12, MathSciNet.  
  6. Applications of Fibonacci numbers. Vol. 7. Proceedings of the 7th International Research Conference on Fibonacci Numbers and their Applications held at the Technische Universität Graz, Graz, July 15--19, 1996.
    Edited by G. E. Bergum, A. N. Philippou and A. F. Horadam.
    Kluwer Academic Publishers, Dordrecht, 1998. xxxvi+484 pp. ISBN: 0-7923-5022-7, MathSciNet.  
  7. An algorithm for searching for the minimum of unimodal functions of several variables. (Russian)  
    Glotov, P. E.
    Vestnik Moskov. Univ. Ser. XV Vychisl. Mat. Kibernet.  1998,  no. 4, 28--30, 51, MathSciNet.  
  8. The golden ratio and Fibonacci numbers.
    Dunlap, Richard A.
    World Scientific Publishing Co., Inc., River Edge, NJ, 1997. viii+162 pp. ISBN: 981-02-3264-0 11B39, MathSciNet.  
  9. Applications of Fibonacci numbers. Vol. 6. Proceedings of the Sixth International Research Conference on Fibonacci Numbers and their Applications held at Washington State University, Pullman, Washington, July 18--22, 1994.
    Edited by G. E. Bergum, A. N. Philippou and A. F. Horadam.
    Kluwer Academic Publishers Group, Dordrecht, 1996. xxviii+551 pp. ISBN: 0-7923-3956-8 11-06, MathSciNet.  
  10. On Some Applications of Fibonacci Numbers (in The Computer Science Sampler)  
    David L. Ranum  
    The American Mathematical Monthly, Vol. 102, No. 7. (Aug. - Sep., 1995), pp. 640-645, Jstor.  
  11. On an optimal procedure for searching for the global extremum of a locally unimodal function. (Russian)
    Suprun, A. N.
    Zh. Vychisl. Mat. i Mat. Fiz. 35 (1995), no. 5, 788--794; translation in Comput. Math. Math. Phys. 35 (1995), no. 5, 623--627, MathSciNet.  
  12. A Fibonacci Version of Kraft's Inequality Applied to Discrete Unimodal Search.
    Goldstein, Arthur S.; Reingold, Edward M.
    Siam journal on computing, 1993, vol. 22, no. 4, pp. 751--777, Ingenta.
  13. One Dimensional Nonlinear Search Algorithms: Macros for Fibonacci's Search Method
    Fox
    Computers in education journal, 1993, vol. 3, no. 3, pp. 60, Ingenta.
  14. On the Complexity of Search Algorithms  
    Kuo-Liang Chung, Wen-Chin Chen, Ferng-Ching Lin  
    IEEE Transactions on Computers, September 1992 (Vol. 41, No. 9), pp.  1172-1176
  15. The Fibonacci search for cornerpoint detection of two-dimensional images.
    Lee, J.D.; Chen, C.H.; Lee, J.Y.
    Mathematical and computer modelling, 1992, vol. 16, no. 11, pp. 15, Ingenta.
  16. Optimization problems with unimodal functions in max-separable constraints.
    Zimmermann, K.
    Optimization 24 (1992), no. 1-2, 31--41, MathSciNet.  
  17. Generalization of the Fibonacci search
    Capocelli, Renato M.
    Proceedings of the International Conference on Fibonacci Numbers and Their Applications, v 4, 1991, p 69--76, Compendex.
  18. Max-separable optimization problems with unimodal functions.
    Zimmermann, Karel
    Ekonom.-Mat. Obzor 27 (1991), no. 2, 159--169, MathSciNet.  
  19. Applications of Fibonacci numbers. Vol. 4. Proceedings of the Fourth International Conference on Fibonacci Numbers and their Applications held at Wake Forest University, Winston-Salem, North Carolina, July 30--August 3, 1990.
    Edited by G. E. Bergum, A. N. Philippou and A. F. Horadam.
    Kluwer Academic Publishers Group, Dordrecht, 1991. xxiv+313 pp. ISBN: 0-7923-1309-7 11-06, MathSciNet.  
  20. On even Fibonacci pseudoprimes.
    Somer, Lawrence
    Applications of Fibonacci numbers, Vol. 4 (Winston-Salem, NC, 1990), 277--288, Kluwer Acad. Publ., Dordrecht, 1991, MathSciNet.  
  21. Extended Fibonacci search for proper sinusoidal functions.    
    Foulds, L. R.; Yu, W.    
    System modelling and optimization (Leipzig, 1989), 124--133, Lecture Notes in Control and Inform. Sci., 143, Springer, Berlin, 1990, MathSciNet.  
  22. Fibonacci & Lucas numbers, and the golden section. Theory and applications.
    Vajda, S.
    Ellis Horwood Series: Mathematics and its Applications. Ellis Horwood Ltd., Chichester; Halsted Press [John Wiley & Sons, Inc.], New York, 1989. 190 pp. ISBN: 0-470-21508-9, MathSciNet.  
  23. A Fibonacci search technique for model parameter selection.
    Vardavas, I. M.
    Ecological modelling, 1989, vol. 48, no. 1/2, pp. 65 , Ingenta.
  24. Fibonacci Numbers and Computer Algorithms (in Computer Corner)  
    John Atkins; Robert Geist  
    The College Mathematics Journal, Vol. 18, No. 4. (Sep., 1987), pp. 328-336, Jstor.  
  25. Binary search revisited: another advantage of Fibonacci search.    
    Nishihara, Seiichi; Nishino, Hiroji     
    IEEE Trans. Comput. 36 (1987), no. 9, 1132--1135, MathSciNet.  
  26. An entropic approach to the optimum search for the optimum of a unimodal function.    
    Guiasu, Silviu    
    Inform. Sci. 42 (1987), no. 1, 69--82, MathSciNet.  
  27. TRANSYT traffic engineering program efficiency improvement via Fibonacci search
    Foulds, L. R.  
    Transportation Research. Part A, General v. 20A (July '86) p. 331-335, FirstSearch.  
  28. A property of the Fibonacci search method. (Chinese)    
    Luo, Sheng Zheng    
    J. Harbin Inst. Tech. 1986, no. 3, 1--6, MathSciNet.  
  29. Minimizing a unimodal function of two integer variables.
    Hoffman, Alan J.; Wolfe, Philip
    Mathematical programming, II. Math. Programming Stud. No. 25 (1985), 76--87, MathSciNet.  
  30. Wythoff games, continued fractions, cedar trees and Fibonacci searches.    
    Fraenkel, Aviezri S.    
    Theoret. Comput. Sci. 29 (1984), no. 1-2, 49--73, MathSciNet.  
  31. A simple proof of the optimality of the parallel Fibonacci sequential search method. (Chinese)    
    Han, Ji Ye    
    Qufu Shiyuan Xuebao 1984, no. 1, 1--7, MathSciNet.  
  32. Optimal methods of integration of unimodal functions. (Russian)
    Korchanov, S. V.
    Vestnik Moskov. Univ. Ser. XV Vychisl. Mat. Kibernet. 1984, no. 3, 38--43, MathSciNet.  
  33. Optimal search for an extremum of locally unimodal functions.     
    Tarasova, V. P.    
    Cybernetics 20 (1984), no. 1, 98--104; translated from Kibernetika (Kiev) 1984, , no. 1, 65--68(Russian), MathSciNet.  
  34. Wythoff games, continued fractions, cedar trees and Fibonacci searches.
    Fraenkel, Aviezri S.
    Automata, languages and programming (Barcelona, 1983), 203--225, Lecture Notes in Comput. Sci., 154, Springer, Berlin, 1983, MathSciNet.  
  35. The search for the extremum of a unimodal function of one variable on an unbounded set. (Russian)
    Rubal'skii, G. B.
    Zh. Vychisl. Mat. i Mat. Fiz. 22 (1982), no. 1, 10--16, 251, MathSciNet.  
  36. On maximizing functions by Fibonacci search.    
    Hassin, Refael    
    Fibonacci Quart. 19 (1981), no. 4, 347--351, MathSciNet.  
  37. A non-Fibonacci search plan with Fibonacci-like results.   
    Hill, Robert R.; Goldstein, Kenneth L.    
    Fibonacci Quart. 19 (1981), no. 2, 131--136, MathSciNet.  
  38. Analysis of the generalized Fibonacci search method.    
    O'Reilly, Thomas J.    
    Proceedings of the Twelfth Southeastern Conference on Combinatorics, Graph Theory and Computing, Vol. II (Baton Rouge, La., 1981). Congr. Numer. 33 (1981), 275--284, MathSciNet.  
  39. An application of the Fibonacci search technique to determine optimal sample size in a Bayesian decision problem.    
    Braverman, Jerome D.; Toof, David J.    
    A collection of manuscripts related to the Fibonacci sequence, pp. 137--145, Fibonacci Assoc., Santa Clara, Calif., 1980, MathSciNet.  
  40. A collection of manuscripts related to the Fibonacci sequence. 18th anniversary volume of the Fibonacci Association.
    Edited by Verner E. Hoggatt, Jr. and Marjorie Bicknell-Johnson.
    Fibonacci Association, Santa Clara, Calif., 1980. vi+229 pp. 10-06, MathSciNet.  
  41. Effective second-order methods of minimizing of unimodal functions. (Russian)
    Evdokimov, A. G.; Melesko, V. I.
    Operations research (models, systems, solutions), No. 7 (Russian), pp. 100--111, 2, Akad. Nauk SSSR, Vychisl. Tsentr, Moscow, 1979, MathSciNet.  
  42. Search for minima of some unimodal functions. (Russian)
    Korotcenko, A. G.
    Zh. Vychisl. Mat. i Mat. Fiz. 19 (1979), no. 5, 1337--1340, 1360, MathSciNet.  
  43. Primitive periods of generalized Fibonacci sequences.
    Smith, Claudia; Hoggatt, Verner E., Jr.
    Fibonacci Quart. 14 (1976), no. 4, 343--347, MathSciNet.  
  44. Assembly-line balancing: zero-one programming with Fibonacci search.   
    Patterson, James H.; Albracht, Joseph J.    
    Operations Res. 23 (1975), no. 1, 166--172, MathSciNet.  
  45. Repeated binomial coefficients and Fibonacci numbers.
    Singmaster, David
    Fibonacci Quart. 13 (1975), no. 4, 295--298, MathSciNet.  
  46. Efficiency of the Fibonacci search method.    
    Overholt, K. J.    
    Nordisk Tidskr. Informationsbehandling (BIT) 13 (1973), 92--96, MathSciNet.  
  47. Fibonacci search with arbitrary first evaluation.    
    Witzgall, Christoph    
    Fibonacci Quart. 10 (1972), no. 2, 113--134, 146.
  48. Optimal algorithms for minimization in a class of unimodal functions. (Ukrainian)
    Ivanov, V. V.; Kijasko, G. A.
    Dopovidi Akad. Nauk Ukraïn. RSR Ser. A 1972, 313--316, 380, MathSciNet.  
  49. Optimal search for the extremum of unimodal functions. (Russian)  
    Cernous'ko, F. L.
    Z. Vycisl. Mat. i Mat. Fiz. 10 (1970), 922--933, MathSciNet.  
  50. Minimax optimization of unimodal functions by variable block search.    
    Beamer, John H.; Wilde, D. J.    
    Management Sci. 16 1969/1970 529--541, MathSciNet.  
  51. A generalization of Fibonacci search to the multidimensional case. (Russian)    
    Kuzovkin, A. I.    
    Èkonom. i Mat. Metody 4 1968 931--940, MathSciNet.  
  52. Optimality proof for the symmetric Fibonacci search technique.   
    Avriel, Mordecai; Wilde, Douglass J.    
    Fibonacci Quart. 4 1966 265--269, MathSciNet.  
  53. Optimum search for the location of the maximum of a unimodal function.
    Fine, Terrence
    IEEE Trans. Information Theory IT-12 1966 103--111, MathSciNet.  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004