Bibliography for Nonlinear Systems

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  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. 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.
  3. 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.  
  4. 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.  
  5. 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.
  6. 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.  
  7. Numerical experience with Newton-like methods for nonlinear algebraic systems.    
    Spedicato, E.; Huang, Z.    
    Computing 58 (1997), no. 1, 69--89, MathSciNet.  
  8. 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.
  9. 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.  
  10. Sor-Secant Methods  
    Jose Mario Martinez  
    SIAM Journal on Numerical Analysis, Vol. 31, No. 1. (Feb., 1994), pp. 217-226, Jstor.  
  11. Fixed-Point Quasi-Newton Methods   
    Jose Mario Martinez   
    SIAM Journal on Numerical Analysis, Vol. 29, No. 5. (Oct., 1992), pp. 1413-1434, Jstor.  
  12. 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.
  13. 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.  
  14. 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.  
  15. A special extended system and a Newton-like method for simple singular nonlinear equations.   
    Mei, Z.    
    Computing 45 (1990), no. 2, 157--167, MathSciNet.  
  16. A generalisation of the interval Newton single-step method for nonlinear systems of equations.    
    Thiel, Siegfried    
    Computing 43 (1989), no. 1, 73--84, MathSciNet.  
  17. 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.  
  18. Attracting Orbits in Newton's Method  
    Mike Hurley  
    Transactions of the American Mathematical Society, Vol. 297, No. 1. (Sep., 1986), pp. 143-158, Jstor.  
  19. 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.
  20. 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.
  21. Quasi-Newton Updates in Abstract Vector Spaces  
    Michael J. Todd
    SIAM Review, Vol. 26, No. 3. (Jul., 1984), pp. 367-377, Jstor.
  22. 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.  
  23. 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.  
  24. 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.  
  25. 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.  
  26. 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.  
  27. Revision of a Derivative-Free Quasi-Newton Method   
    John Greenstadt   
    Mathematics of Computation, Vol. 32, No. 141. (Jan., 1978), pp. 201-221, Jstor.  
  28. 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.  
  29. 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.  
  30. 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.  
  31. 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.  
  32. 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.  
  33. 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.
  34. A Quasi-Newton Method with No Derivatives  
    John Greenstadt
    Mathematics of Computation, Vol. 26, No. 117. (Jan., 1972), pp. 145-166, Jstor.  
  35. 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.  
  36. The Convergence of Single-Rank Quasi-Newton Methods   
    C. G. Broyden   
    Mathematics of Computation, Vol. 24, No. 110. (Apr., 1970), pp. 365-382, Jstor.  
  37. 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.  
  38. 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.  
  39. 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