1. A Characteristic Condition for Convergence of Steepest Descent Approximation to Accretive Operator Equations
   Gao, G.-l.; Zhou, H.-y.
   Journal- Hebei Normal University Natural Science Edition, 2003, vol. 27, no. 3, pp. 231-234, Ingenta.  
2. Application of Steepest Descent Method in Determination of Parameters in Rainstorm Intensity Formula
   Zhang, Y.
   China Water and Wastewater, 2003, vol. 19, no. 2, pp. 67-69, Ingenta.  
3. A steepest descent algorithm for circularity evaluation
   Zhu, L. M.; Ding, H.; Xiong, Y. L.
   Computer Aided Design, 2003, vol. 35, no. 3, pp. 255-265, Ingenta.  
4. A characteristic condition for convergence of steepest descent approximation to accretive operator equations
   Zhou, H.
   Journal of Mathematical Analysis and Applications, 2002, vol. 271, no. 1, pp. 1-6, Ingenta.  
5. Purification of the first-order density matrix using steepest descent and Newton-Raphson methods
   Pino, R.; Scuseria, G. E.
   Chemical Physics Letters, 2002, vol. 360, no. 1-2, pp. 117-122, Ingenta.  
6. Stability of Steepest Descent With Momentum for Quadratic Functions
   Torii, M.; Hagan, M. T.
   IEEE Transactions on Neural Networks, 2002, vol. 13, no. 3, pp. 752-756, Ingenta.  
7. Parallel Implementation of the Steepest Descent Fast Multipole Method (SDFMM) on a Beowulf Cluster for Subsurface Sensing Applications
   Jiang, D.; Meleis, W.; El-Shenawee, M.; Mizan, E.; Ashouei, M.; Rappaport, C.
   IEEE Microwave and Wireless Components Letters, 2002, vol. 12, no. 1, pp. 24-26, Ingenta.  
8. The convergence properties of a class of new conjugate gradient methods with some types of inexact line searches.    
   Liang, Yu-mei; Liu, Yun    
   J. Guangxi Univ. Nat. Sci. Ed. 26 (2001), no. 2, 133--136, MathSciNet.  
9. Monte Carlo simulations of electromagnetic wave scattering from a random rough surface with three-dimensional penetrable buried object: mine detection application using the steepest-descent fast multipole method
   El-Shenawee, M.; Rappaport, C.; Silevitch, M.
   Journal- Optical Society of America A, 2001, vol. 18, no. 12, pp. 3077-3084, Ingenta.  
10. A Parallel ADI and Steepest Descent Methods
    Schevtschenko, I. V.
    Lecture Notes in Computer Science, 2001, no. 2131, pp. 265-271, Ingenta.  
11. The spherical quadratic steepest descent (SQSD) method for unconstrained minimization with no explicit line searches
    Snyman, J. A.; Hay, A. M.
    Computers and Mathematics With Applications, 2001, vol. 42, no. ER1-2, pp. 169-178, Ingenta.  
12. Steepest descent methods for multicriteria optimization.    
    Fliege, Jörg; Svaiter, Benar Fux    
    Math. Methods Oper. Res. 51 (2000), no. 3, 479--494, MathSciNet.  
13. Characteristic conditions for convergence of generalized steepest descent approximation to multivalued accretive operator equations.    
    Zhou, Haiyun; Cho, Yeol Je; Kang, Shin Min    
    Comput. Math. Appl. 39 (2000), no. 3-4, 1--11, MathSciNet.  
14. A gradient search interpretation of the super-exponential algorithm.    
    Mboup, Mamadou; Regalia, Phillip A.    
    IEEE Trans. Inform. Theory 46 (2000), no. 7, 2731--2734.
15. A CMA adaptive array with digital phase shifters by a genetic algorithm and a steepest descent method
    Kimura, Y.; Hirasawa, K.
    IEEE Antennas and Propagation Society International Symposium, 2000, vol. 2, pp. 914-917, Ingenta.  
16. Steepest descent using smoothed gradients.
    Richardson Jr., W.B.
    Applied Mathematics and Computation, 2000, vol. 112, no. 2/3, pp. 241, Ingenta.  
17. The influence of the largest eigenvalues on the numerical convergence of the conjugate gradient method. (Russian)
    Eremin, A. Yu.; Kaporin, I. E.
    Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 248 (1998), Chisl. Metody i Vopr. Organ. Vychisl. 13, 5--16, 247; translation in J. Math. Sci. (New York) 101 (2000), no. 4, 3231--3236, MathSciNet.  
18. Steepest descent evolution equations: asymptotic behavior of solutions and rate of convergence.    
    Cominetti, R.; Alemany, O.    
    Trans. Amer. Math. Soc. 351 (1999), no. 12, 4847--4860, MathSciNet.  
19. Optimization with constraints using the chaos steepest descent method. (Japanese)
    Ishigame, Atsushi; Aihara, Tohru; Yuasa, Hidetaka
    Trans. Inst. Systems Control Inform. Engrs. 12 (1999), no. 5, 316--318, MathSciNet.  
20. An enhanced response surface methodology (RSM) algorithm using gradient deflection and second-order search strategies.    
    Joshi, Shirish; Sherali, Hanif D.; Tew, Jeffrey D.    
    Comput. Oper. Res. 25 (1998), no. 7-8, 531--541, MathSciNet.  
21. A class of new conjugate gradient methods with inexact line searches.    
    Li, Rongsheng; Liu, Guanghui     
    Adv. in Math. (China) 26 (1997), no. 1, 29--35, MathSciNet.  
22. The origin of the method of steepest descent.    
    Petrova, Svetlana S.; Solovprime ev, Alexander D.    
    Historia Math. 24 (1997), no. 4, 361--375, MathSciNet.  
23. Behavior of the Steepest Descent Method in Minimizing Rayleigh Quotient.
    Ozeki, Takashi; Iijima, Taizo
    IEICE transactions on fundamentals of electronics, communications and computer sciences, 1997, vol. 80, no. 1, pp. 176, Ingenta.  
24. Steepest Descent Methods with Generalized Distances for Constrained Optimization.
    Iusem, Alfredo N.
    Acta applicandae mathematicae, 1997, vol. 46, no. 2, pp. 225, Ingenta.  
25. A new global optimization algorithm based upon gradient search. (Chinese)    
    Zheng, Li Hui; Guo, Ya Jun; Pan, De Hui    
    Control Theory Appl. 14 (1997), no. 3, 343--348, MathSciNet.  
26. Convergence of the steepest descent method for minimizing quasiconvex functions.
    Kiwiel, K. C.; Murty, K.
    J. Optim. Theory Appl. 89 (1996), no. 1, 221--226, MathSciNet.  
27. Use of steepest descent for certain quadratic constraints.    
    Kim, Keehwan    
    Far East J. Math. Sci. 4 (1996), no. 3, 443--451, MathSciNet.  
28. Convergence of the Steepest Descent Method for Minimizing Quasiconvex Functions.
    Kiwiel, K.C.; Murty, K.
    Journal of optimization theory and applications, 1996, vol. 89, no. 1, pp. 221, Ingenta.  
29. Full Convergence of the Steepest Descent Method with Inexact Line Searches.
    Burachik, R.; Drummond, L.M.G.; Svaiter, B.F.
    Optimization, 1995, vol. 32, no. 2, pp. 137--146, Ingenta.  
30. A rectified steepest descent method for solving unconstrained optimization problems. (Chinese)
    Fu, Wen Jun
    Neimenggu Daxue Xuebao Ziran Kexue 26 (1995), no. 1, 28--33, MathSciNet.  
31. Steepest Descent Algorithms for Neural Network Controllers and Filters.
    Piche, S.W.
    IEEE transactions on neural networks, 1994, vol. 5, no. 2, pp. 198, Ingenta.  
32. A Steepest Descent Method for Oscillatory Riemann--Hilbert Problems. Asymptotics for the MKdV Equation  
    P. Deift, X. Zhou  
    The Annals of Mathematics, 2nd Ser., Vol. 137, No. 2. (Mar., 1993), pp. 295-368, Jstor.  
33. On the Identification Property of a Projected Gradient Method  
    P. L. De Angelis; G. Toraldo  
    SIAM Journal on Numerical Analysis, Vol. 30, No. 5. (Oct., 1993), pp. 1483-1497, Jstor.  
34. On the Identification Property of a Projected Gradient Method
    P. L. De Angelis, G. Toraldo
    SIAM Journal on Numerical Analysis, Vol. 30, No. 5. (Oct., 1993), pp. 1483-1497, Jstor.  
35. New adaptive algorithms based on the method of steepest descent.
    Arunachalam, K.G.; Chesmore, E.D.
    International journal of electronics, 1993, vol. 74, no. 1, pp. 1, Ingenta.  
36. An interactive multi-objective gradient search.    
    Ringuest, Jeffrey L.; Gulledge, Thomas R.    
    Oper. Res. Lett. 12 (1992), no. 1, 53--58, MathSciNet.  
37. Rapid learning method for multilayered neural networks using two-dimensional conjugate gradient search.    
    Yoshida, Toshinobu    
    J. Inform. Process. 15 (1992), no. 1, 79--86.
38. Suboptimal Control: Steepest Descent with Respect to the Lagrangian.
    Afanas'ev, V.N.; Tsomaeva, E.A.
    Automation and remote control, 1992, vol. 53, no. 11p1, pp. 1679, Ingenta.  
39. The asymptotic behaviour of the three-step method of steepest descent.
    Zhuk, P.F.
    Computational mathematics and mathematical physics, 1992, vol. 32, no. 3, pp. 419, Ingenta.  
40. On the Global Convergence of Trust Region Algorithms Using Inexact Gradient Information
    Richard G. Carter
    SIAM Journal on Numerical Analysis, Vol. 28, No. 1. (Feb., 1991), pp. 251-265, Jstor.  
41. Maximum Length of Steepest Descent Curves for Quasi-Convex Functions.
    Manselli, Paolo
    Geometriae dedicata, 1991, vol. 38, no. 2, pp. 211, Ingenta.  
42. On Functions Whose Curves of Steepest Descent Are Straight Lines.
    Magnanini, Rolando
    Applicable analysis, 1991, vol. 41, no. 1/4, pp. 171, Ingenta.  
43. Application of gradient search algorithms for studying the stability of nonlinear difference systems. (Russian)    
    Khusainov, D. Ya.; Stadnik, O. I.    
    Vychisl. Prikl. Mat. (Kiev) No. 75 (1991), 35--38; translation in J. Math. Sci. 72 (1994), no. 3, 3073--3075, MathSciNet.  
44. Conjugate gradient methods using quasi-Newton updates with inexact line searches.    
    Sherali, Hanif D.; Ulular, Osman    
    J. Math. Anal. Appl. 150 (1990), no. 2, 359--377, MathSciNet.  
45. A trajectory algorithm based on the gradient method. I. The search on the quasioptimal trajectories.    
    Sturua, E. G.; Zavriev, S. K.     
    2nd IIASA Workshop on Global Optimization (Sopron, 1990). J. Global Optim. 1 (1991), no. 4, 375--388, MathSciNet.  
46. The steepest descent gravitational method for linear programming.
    Chang, S.Y.; Murty, K.G.
    Discrete applied mathematics and combinatorial operations research, 1989, vol. 25, no. 3, pp. 211, Ingenta.  
47. Nonorthogonal Analysis of Variance Using Gradient Methods (in Theory and Methods)  
    Mortaza Jamshidian; Robert I. Jennrich  
    Journal of the American Statistical Association, Vol. 83, No. 402. (Jun., 1988), pp. 483-489, Jstor.  
48. A Stochastic Steepest-Descent Algorithm.
    Wardi, Y.
    Journal of optimization theory and applications, 1988, vol. 59, no. 2, pp. 307, Ingenta.  
49. Numerical experiments by the reduced gradient method in linearly constrained minimization.
    Gaviano, M.; Milia, D.; Testa, F.
    Rend. Sem. Fac. Sci. Univ. Cagliari 58 (1988), no. 1-2, 19--41, MathSciNet.  
50. A numerical comparison of conjugate gradient-like methods.
    Langtangen, Hans Petter; Tveito, Aslak
    Comm. Appl. Numer. Methods 4 (1988), no. 6, 793--798, MathSciNet.  
51. A Trust Region Algorithm for Equality Constrained Minimization: Convergence Properties and Implementation  
    Avi Vardi  
    SIAM Journal on Numerical Analysis, Vol. 22, No. 3. (Jun., 1985), pp. 575-591, Jstor.  
52. Intelligent gradient search in linear programming.   
    Nickels, W.; Rödder, W.; Xu, L.; Zimmermann, H.-J.    
    European J. Oper. Res. 22 (1985), no. 3, 293--303.
53. A numerical study of various algorithms related to the preconditioned conjugate gradient method.
    Jackson, C. P.; Robinson, P. C.
    Internat. J. Numer. Methods Engrg. 21 (1985), no. 7, 1315--1338, MathSciNet.  
54. On the steepest-descent method for a class of quasidifferentiable optimization problems.
    Pallaschke, D.; Recht, P.
    Nondifferentiable optimization: motivations and applications (Sopron, 1984), 252--263, Lecture Notes in Econom. and Math. Systems, 255, Springer, Berlin, 1985, MathSciNet.  
55. Newton-Type Minimization Via the Lanczos Method  
    Stephen G. Nash  
    SIAM Journal on Numerical Analysis, Vol. 21, No. 4. (Aug., 1984), pp. 770-788, Jstor.  
56. Use of a nonquadratic model in a conjugate-gradient method of optimization with inexact line searches.   
    Tassopoulos, A.; Storey, C.    
    J. Optim. Theory Appl. 43 (1984), no. 3, 357--370, MathSciNet.  
57. Gradient Method for Nondensely Defined Closed Unbounded Linear Operators  
    Sung J. Lee; M. Zuhair Nashed  
    Proceedings of the American Mathematical Society, Vol. 88, No. 3. (Jul., 1983), pp. 429-435, Jstor.  
58. The Conjugate Gradient Method and Trust Regions in Large Scale Optimization
    Trond Steihaug
    SIAM Journal on Numerical Analysis, Vol. 20, No. 3. (Jun., 1983), pp. 626-637, Jstor.  
59. An Efficient Method to Solve the Minimax Problem Directly  
    C. Charalambous; A. R. Conn  
    SIAM Journal on Numerical Analysis, Vol. 15, No. 1. (Feb., 1978), pp. 162-187, Jstor.  
60. Conjugate gradient methods with inexact searches.    
    Shanno, David F.    
    Math. Oper. Res. 3 (1978), no. 3, 244--256, MathSciNet.  
61. On the convergence behaviour of two conjugate gradient methods for which the line searches are inaccurate.   
    Gaviano, M.; Buttu, A.    
    Rend. Sem. Fac. Sci. Univ. Cagliari 47 (1977), no. 3-4, 289--304, MathSciNet.  
62. A steepest-descent method for optimization of mechanical systems.
    Haug, E. J.; Arora, J. S.; Matsui, K.
    J. Optimization Theory Appl. 19 (1976), no. 3, 401--424, MathSciNet.  
63. An Historical Survey of Computational Methods in Optimal Control  
    E. Polak  
    SIAM Review, Vol. 15, No. 2, Part 2: Anniversary Supplement. (Apr., 1973), pp. 553-584, Jstor.  
64. Rate of Convergence of Several Conjugate Gradient Algorithms
    Arthur I. Cohen
    SIAM Journal on Numerical Analysis, Vol. 9, No. 2. (Jun., 1972), pp. 248-259.
65. Remarks on the comparison between random search methods and the gradient method.    
    Gaviano, Marco; Fagiuoli, Enrico    
    Minimization algorithms, mathematical theories and computer results (Proc. Sem., Math. Inst., Univ. Cagliari, Cagliari, 1971), pp. 337--349, MathSciNet.  
66. Steepest Descent for Singular Linear Operator Equations  
    M. Z. Nashed  
    SIAM Journal on Numerical Analysis, Vol. 7, No. 3. (Sep., 1970), pp. 358-362, Jstor.  
67. Conditioning of Quasi-Newton Methods for Function Minimization  
    D. F. Shanno  
    Mathematics of Computation, Vol. 24, No. 111. (Jul., 1970), pp. 647-656, Jstor.  
68. Comparison of Gradient Methods for the Solution of Nonlinear Parameter Estimation Problems  
    Yonathan Bard  
    SIAM Journal on Numerical Analysis, Vol. 7, No. 1. (Mar., 1970), pp. 157-186, Jstor.  
69. Variational approach to the gradient method: Theory and numerical experiments.
    Miele, Angelo
    1969 Computing Methods in Optimization Problems (Second Internat. Conf., San Remo, 1968) pp. 143--157 Springer, Berlin, MathSciNet.  
70. Two Algorithms Related to the Method of Steepest Descent  
    T. M. Whitney, R. K. Meany  
    SIAM Journal on Numerical Analysis, Vol. 4, No. 1. (Mar., 1967), pp. 109-118, Jstor.  
71. On the Relative Efficiencies of Gradient Methods  
    John Greenstadt  
    Mathematics of Computation, Vol. 21, No. 99. (Jul., 1967), pp. 360-367, Jstor.  
72. Improvement of steepest-descent method for optimizing control systems. (Japanese)
    Fujii, Katsuhiko; Nishimura, Yukio; Taguchi, Hideo
    J. Japan Assoc. Automat. Control Engrs. 11 1967 38--43, MathSciNet.  
73. A Ricocheting Gradient Method for Nonlinear Optimization  
    J. L. Greenstadt  
    SIAM Journal on Applied Mathematics, Vol. 14, No. 3. (May, 1966), pp. 429-445, Jstor.  
74. Maximization by Quadratic Hill-Climbing  
    Stephen M. Goldfeld; Richard E. Quandt; Hale F. Trotter  
    Econometrica, Vol. 34, No. 3. (Jul., 1966), pp. 541-551, Jstor.  
75. The Circles of Curvature of the Curves of Steepest Descent of Green's Function  
    J. L. Walsh  
    The American Mathematical Monthly, Vol. 68, No. 4. (Apr., 1961), pp. 323-329, Jstor.  
76. On the Optimum Gradient Method for Systems of Linear Equations  
    M. Marcus  
    Proceedings of the American Mathematical Society, Vol. 7, No. 1. (Feb., 1956), pp. 77-81, Jstor.  

(c) John H. Mathews 2004