Bibliography for Nonlinear Systems

unabridged

 

  1. The Newton-arithmetic mean method for the solution of systems of nonlinear equations
    Galligani, Emanuele
    Applied Mathematics and Computation, v 134, n 1, Jan 10, 2003, p 9-34, Compendex.
  2. Applications of natural level functions in damped Newton method for ill-conditioned systems of nonlinear equations
    Zeng, Jin-Ping; Liu, Xing-Guo
    Hunan Daxue Xuebao/Journal of Hunan University Natural Sciences, v 30, n 1, February, 2003, p 8, Compendex.
  3. A globally convergent Newton-GMRES subspace method for systems of nonlinear equations
    Bellavia, Stefania; Morini, Benedetta
    SIAM Journal of Scientific Computing, v 23, n 3, 2002, p 940-960, Compendex.
  4. An efficient implementation scheme of the simplified Newton iteration for block systems of nonlinear equations.    
    Zhao, Shuangsuo
    Appl. Numer. Math. 39 (2001), no. 2, 225--237, MathSciNet.  
  5. Convergent regions of the Newton homotopy method for nonlinear systems: theory and computational applications
    Lee, Jaewook; Chiang, Hsiao-Dong
    IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, v 48, n 1, Jan, 2001, p 51-66, Compendex.
  6. Inexact Quasi-Newton methods for sparse systems of nonlinear equations
    Bergamaschi, L.; Moret, I.; Zilli, G.
    Future Generation Computer Systems, v 18, n 1, September, 2001, p 41-53, Compendex.
  7. A globally convergent Newton-GMRES subspace method for systems of nonlinear equations.    
    Bellavia, Stefania; Morini, Benedetta    
    SIAM J. Sci. Comput. 23 (2001), no. 3, 940--960 (electronic), MathSciNet.  
  8. Synchronous and asynchronous interval Newton-Schwarz methods for a class of large systems of nonlinear equations.    
    Schwandt, Hartmut    
    Reliab. Comput. 7 (2001), no. 4, 281--306, MathSciNet.  
  9. Convergence acceleration of a general Newton method for systems of nonlinear equations.    
    Luzanin, Zorana; Rapaji'c, Sanja    
    Sci. Math. Jpn. 54 (2001), no. 3, 513--519, MathSciNet.  
  10. Complex coefficient Newton method and its application in dynamic simulation of power system
    Zhou, B.; Fang, D. Z.; Chung, T. S.
    IEE Conference Publication, 2000, no. 478, pp. 469-472, Ingenta.  
  11. Problem of phase distortion correction by the Newton modified method in the adaptive optical system
    Degtyarev, G.; Makhan ko, A. V.; Chernyavskii, S.; Chernyavskii, A.
    Proceedings- Spie the International Society for Optical Engineering, 2000, no. 4341, pp. 161-172, Ingenta.  
  12. Globally convergent inexact-Newton method for solving reducible nonlinear systems of equations
    Krejic, Natasa; Martinez, Jose Mario
    Optimization Methods and Software, v 13, n 1, 2000, p 11-34, Compendex.
  13. Practical quasi-Newton methods for solving nonlinear systems.
    Martínez, José Mario    
    Numerical analysis 2000, Vol. IV, Optimization and nonlinear equations. J. Comput. Appl. Math. 124 (2000), no. 1-2, 97--121, MathSciNet.  
  14. Finite difference Newton's method for systems of nonlinear equations
    Weerakoon, S.; Amarasekera, H.K.G. De Z.
    Mathematical Engineering in Industry, v 7, n 4, 1999, p 433-440, Compendex.
  15. Convergence of partially asynchronous block quasi-Newton methods for nonlinear systems of equations
    Xu, Jian-Jun
    Journal of Computational and Applied Mathematics, v 103, n 2, Mar, 1999, p 307-321, Compendex.
  16. Parallel Newton methods for sparse systems of nonlinear equations.   
    Zilli, Giovanni; Bergamaschi, Luca    
    Proceedings of the Workshop "Numerical Methods in Optimization" (Cortona, 1997). Rend. Circ. Mat. Palermo (2) Suppl. 1999, no. 58, 247--257, MathSciNet.  
  17. Newton generalized Hessenberg method for solving nonlinear systems of equations.   
    Heyouni, M.
    Numerical methods for partial differential equations (Marrakech, 1998), MathSciNet.  
  18. A general Newton method for systems of nonlinear equations. II.    
    Noda, Tatsuo; Ishii, Hiroaki     
    Math. Japon. 48 (1998), no. 3, 447--452.
  19. On the convergence of the quasi-Gauss-Newton methods for solving nonlinear systems.    
    Albeanu, Grigore    
    Int. J. Comput. Math. 66 (1998), no. 1-2, 93--99, MathSciNet.  
  20. Accelerated inexact Newton schemes for large systems of nonlinear equations.    
    Fokkema, Diederik R.; Sleijpen, Gerard L. G.; Van der Vorst, Henk A.  
    SIAM J. Sci. Comput. 19 (1998), no. 2, 657--674 (electronic), MathSciNet.  
  21. A class of discretized Newton methods for solving systems of nonlinear equations. (Chinese)    
    Chen, Zhi; Gao, Lu-duan; Deng, Nai-yang    
    Math. Numer. Sin. 20 (1998), no. 1, 57--68, MathSciNet.  
  22. NITSOL: a Newton iterative solver for nonlinear systems.   
    Pernice, Michael; Walker, Homer F.    
    Special issue on iterative methods (Copper Mountain, CO, 1996). SIAM J. Sci. Comput. 19 (1998), no. 1, 302--318 (electronic), MathSciNet.
  23. A Modified Newton Method for Radial Distribution System Power Flow Analysis.
    Zhang, F.; Cheng, C. S.
    Ieee transactions on power systems, 1997, vol. 12, no. 1, pp. 389, Ingenta.  
  24. Truncated block Newton and quasi-Newton methods for sparse systems of nonlinear equations. Experiments on parallel platforms
    Zilli, G.; Bergamaschi, L.
    Lecture Notes in Computer Science, v 1332, Recent Advances in Parallel Virtual Machine and Message Passing Interface, 1997, p 390, Compendex.
  25. Numerical experience with Newton-like methods for nonlinear algebraic systems.    
    Spedicato, E.; Huang, Z.    
    Computing 58 (1997), no. 1, 69--89, MathSciNet.  
  26. Selecting the steplength for the Newton method in simulating strongly nonlinear systems
    Godlevskiy, V.S.
    Engineering Simulation, v 13, n 4, 1996, p 593-600, Compendex.
  27. Quasi-inexact-Newton methods with global convergence for solving constrained nonlinear systems.    
    Martínez, José Mario    
    Proceedings of the Second World Congress of Nonlinear Analysts, Part 1 (Athens, 1996). Nonlinear Anal. 30 (1997), no. 1, 1--7, MathSciNet.
  28. A Newton-PCG parallel algorithm for solving systems of nonlinear equations. (Chinese)    
    Zhang, Ru Qing    
    Chinese J. Appl. Mech. 13 (1996), no. 2, 98--102, VII, MathSciNet.  
  29. An improved line search technique in quasi-Newton methods for systems of nonlinear equations. (Chinese)    
    Li, Dong Hui; Zhang, Zhong Zhi    
    Hunan Daxue Xuebao 23 (1996), no. 4, 1--6, MathSciNet.  
  30. On the Efficiency of a Modification of Newton's Method of Solving a System of Equations.
    Sattarov, R.N.; Perfilov, S.N.
    Journal of mathematical sciences., 1995, vol. 73, no. 5, pp. 600, Ingenta.  
  31. Asynchronous parallel Newton's method for solving nonlinear systems of equations
    Xu, Jianjun
    Huazhong Ligong Daxue Xuebao/Journal Huazhong, University of Science and Technology, v 23, n Sup, Nov, 1995, p 193, Compendex.
  32. Sor-Secant Methods  
    Jose Mario Martinez  
    SIAM Journal on Numerical Analysis, Vol. 31, No. 1. (Feb., 1994), pp. 217-226, Jstor.  
  33. On solving a system of integro-functional equations of contact problems with nonlinear friction by Newton's method.
    Babaev, A. A.; Musaev, B. I.
    Doklady. Mathematics / Russian Academy of Sciences, 1994, vol. 48, no. 1, pp. 98, Ingenta.  
  34. Newton-Raphson Method for Accuracy Enhancement of Electro-optical Targeting System.
    Lu, S.-T; Chou, C.; Wu, Y.-P.
    IEE proceedings. A, Science, measurement and technology, 1994, vol. 141, no. 3, pp. 160, Ingenta.  
  35. Power system frequency estimation utilizing the Newton-Raphson method.
    Duric, M.B.; Terzjia, V.V.; Skokljev, I.A.
    Electrical engineering, 1994, vol. 77, no. 3, pp. 221, Ingenta.  
  36. Fixed-Point Quasi-Newton Methods   
    Jose Mario Martinez   
    SIAM Journal on Numerical Analysis, Vol. 29, No. 5. (Oct., 1992), pp. 1413-1434, Jstor.  
  37. Convergence of Newton-like methods for nonlinear systems.   
    Bao, Paul G.; Rokne, J. G.   
    J. Franklin Inst. 329 (1992), no. 4, 743--750, MathSciNet.   
  38. Modified newton-raphson method for solving a system of nonlinear equations in problems of complicated heat exchange
    Malikov, Yu.K.; Lisienko, V.G.; Saplin, A.V.
    Journal of Engineering Physics, v 61, n 3, Mar, 1992, p 1168-1174, Compendex.
  39. Superlinear convergence theorems for Newton-type methods for nonlinear systems of equations
    Abaffy, J.
    Journal of Optimization Theory and Applications, v 73, n 2, May, 1992, p 269-277, Compendex.
  40. 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.  
  41. Modified Newton-Raphson Method for Solving System of Nonlinear Equations in Problems of Complicated Heat Exchange.
    Malikov, Yu. K.; Lisienko, V.G.; Saplin, A.V.
    Journal of engineering physics, 1991, vol. 61, no. 3, pp. 1168, Ingenta.  
  42. Modified Newton iterative method for solving system of nonlinear equations.   
    Podisuk, Maitree    
    Southeast Asian Bull. Math. 15 (1991), no. 2, 123--130, MathSciNet.  
  43. The modified Newton-Rafson method for solving the system of nonlinear equations in complicated heat transfer problems
    Malikov, Yu.K.; Lisienko, V.G.; Saplin, A.V.
    Inzhenerno-Fizicheskii Zhurnal, v 61, n 3, Sep, 1991, p 485-492, Compendex.
  44. Numerical approximation of PDE system fixed-point maps via Newton's method.
    Jerome, J.W.
    Journal of computational and applied mathematics, 1991, vol. 38, pp. 211, Ingenta.  
  45. A Family of Quasi-Newton Methods for Nonlinear Equations with Direct Secant Updates of Matrix Factorizations   
    Jose Mario Martinez   
    SIAM Journal on Numerical Analysis, Vol. 27, No. 4. (Aug., 1990), pp. 1034-1049, Jstor.  
  46. Static and Tracking State Estimation in Power System Using Newton's Method.
    Tripathy, S.C.; Chauhan, D.S.; Prasad, G.D.
    Electric machines and power systems, 1990, vol. 18, no. 2, pp. 97, Ingenta.  
  47. Numerical Solution of System of Random Volterra Integral Equations II: Newton's Method.
    Medhin, N.
    Stochastic analysis and applications, 1990, vol. 8, no. 1, pp. 105, Ingenta.  
  48. A special extended system and a Newton-like method for simple singular nonlinear equations.   
    Mei, Z.    
    Computing 45 (1990), no. 2, 157--167, MathSciNet.  
  49. A generalisation of the interval Newton single-step method for nonlinear systems of equations.    
    Thiel, Siegfried    
    Computing 43 (1989), no. 1, 73--84, MathSciNet.  
  50. Modifikation eines intervallmäßigen Newton-Verfahrens bei nichtlinearen Gleichungssystemen. (German) [A modification of an interval Newton method for systems of nonlinear equations]   
    Herzberger, J. Eine    
    Proceedings of the Annual Scientific Meeting of the GAMM (Vienna, 1988). Z. Angew. Math. Mech. 69 (1989), no. 4, T104--T105, MathSciNet.  
  51. Quasi-Newton Updates with Bounds   
    Paul H. Calamai, Jorge J. More   
    SIAM Journal on Numerical Analysis, Vol. 24, No. 6. (Dec., 1987), pp. 1434-1441, Jstor.  
  52. Attracting Orbits in Newton's Method  
    Mike Hurley  
    Transactions of the American Mathematical Society, Vol. 297, No. 1. (Sep., 1986), pp. 143-158, Jstor.  
  53. 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.
  54. An alternating quasi-Newton method for solving systems of nonlinear equations. (Chinese)    
    Wang, De Ren; Lin, You Ming; Wu, Yu Jiang    
    Lanzhou Daxue Xuebao 21 (1985), no. 3, 1--8, MathSciNet.  
  55. On the Local Convergence of a Quasi-Newton Method for the Nonlinear Programming Problem  
    Thomas F. Coleman; Andrew R. Conn
    SIAM Journal on Numerical Analysis, Vol. 21, No. 4. (Aug., 1984), pp. 755-769, Jstor.
  56. Quasi-Newton Updates in Abstract Vector Spaces  
    Michael J. Todd
    SIAM Review, Vol. 26, No. 3. (Jul., 1984), pp. 367-377, Jstor.
  57. The Newton-Chebyshev method for solving systems of nonlinear equations. (Chinese)   
    Li, Jian Yu    
    Math. Numer. Sinica 6 (1984), no. 2, 159--165, MathSciNet.  
  58. 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.  
  59. A Quasi-Newton Method Employing Direct Secant Updates of Matrix Factorizations  
    George W. Johnson; Nieves H. Austria
    SIAM Journal on Numerical Analysis, Vol. 20, No. 2. (Apr., 1983), pp. 315-325, Jstor.  
  60. Numerical Stability of the Halley-Iteration for the Solution of a System of Nonlinear Equations   
    Annie A. M. Cuyt   
    Mathematics of Computation, Vol. 38, No. 157. (Jan., 1982), pp. 171-179, Jstor.  
  61. On a continuous analogue of Newton's method for solving nonlinear systems of equations. (Russian)    
    Banchev, V. Ts.    
    C. R. Acad. Bulgare Sci. 33 (1980), no. 10, 1329--1331, MathSciNet.  
  62. Some globally converging modifications of the Newton method for solving systems of nonlinear equations. (Russian)   
    Burdakov, O. P.    
    Dokl. Akad. Nauk SSSR 254 (1980), no. 3, 521--523, MathSciNet.  
  63. Least Change Secant Updates for Quasi-Newton Methods   
    J. E. Dennis, Jr., R. B. Schnabel   
    SIAM Review, Vol. 21, No. 4. (Oct., 1979), pp. 443-459, Jstor.  
  64. Approximate solution of a nonlinear system on the basis of the Newton-Kantorovich method. (Russian)    
    Svarichevskaya, N. A.    
    Azerbai dzhan. Gos. Univ. Uchen. Zap. 1979, no. 2, 3--9, MathSciNet.  
  65. On the Convergence of a Quasi-Newton Method for Sparse Nonlinear Systems   
    Binh Lam   
    Mathematics of Computation, Vol. 32, No. 142. (Apr., 1978), pp. 447-451, Jstor.  
  66. Revision of a Derivative-Free Quasi-Newton Method   
    John Greenstadt   
    Mathematics of Computation, Vol. 32, No. 141. (Jan., 1978), pp. 201-221, Jstor.  
  67. On Newton-iterative methods for the solution of systems of nonlinear equations.   
    Sherman, Andrew H.    
    SIAM J. Numer. Anal. 15 (1978), no. 4, 755--771, MathSciNet.  
  68. Quasi-Newton Methods, Motivation and Theory   
    J. E. Dennis, Jr., Jorge J. More   
    SIAM Review, Vol. 19, No. 1. (Jan., 1977), pp. 46-89, Jstor.  
  69. Modification of Newton's method for a nonlinear system. (Hungarian)    
    Gergely, József    
    Alkalmaz. Mat. Lapok 3 (1977), no. 1-2, 199--205, MathSciNet.  
  70. Convergence of Newton-like methods for solving systems of nonlinear equations.    
    Bus, J. C. P.    
    Numer. Math. 27 (1976/77), no. 3, 271--281, MathSciNet.  
  71. A Characterization of Superlinear Convergence and Its Application to Quasi-Newton Methods   
    J. E. Dennis, Jr., Jorge J. More   
    Mathematics of Computation, Vol. 28, No. 126. (Apr., 1974), pp. 549-560, Jstor.  
  72. A modified Newton method for the solution of ill-conditioned systems of nonlinear equations with application to multiple shooting.    
    Deuflhard, P.    
    Numer. Math. 22 (1974), 289--315, MathSciNet.  
  73. Some Efficient Algorithms for Solving Systems of Nonlinear Equations
    Richard P. Brent
    SIAM Journal on Numerical Analysis, Vol. 10, No. 2. (Apr., 1973), pp. 327-344.
  74. A Quasi-Newton Method with No Derivatives  
    John Greenstadt
    Mathematics of Computation, Vol. 26, No. 117. (Jan., 1972), pp. 145-166, Jstor.  
  75. 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.  
  76. The Convergence of Single-Rank Quasi-Newton Methods   
    C. G. Broyden   
    Mathematics of Computation, Vol. 24, No. 110. (Apr., 1970), pp. 365-382, Jstor.  
  77. Modification of a Quasi-Newton Method for Nonlinear Equations with a Sparse Jacobian   
    L. K. Schubert   
    Mathematics of Computation, Vol. 24, No. 109. (Jan., 1970), pp. 27-30, Jstor.  
  78. 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.  
  79. 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.  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004