On The convergence of the quasi-gauss-newton methods for solving nonlinear systems

References

• Albeanu G. The Numerical and Statistical Analysis of the Nonlinear Regression Models. Bucharest 1996 Doctoral Thesis,(in romanian)
   Google Scholar
• Ben-Israel , A. 1966 . A Newton-Raphson method for the solution of equations . J. Math. Anal Appl , 15 : 243 – 252 .
   Web of Science ®Google Scholar
• Broyden , C. G. 1965 . A class of methods for solving nonlinear simultaneous equations . Math. Comput. , 19 : 577 – 593 .
   Web of Science ®Google Scholar
• Broyden , C. G. 1967 . Quasi-Newton methods and their application to function minimization . Math. Comput. , 21 : 368 – 381 .
   Web of Science ®Google Scholar
• Broyden , C. G. , Dennis , J. E. Jr. and Moré Jorje , J. 1973 . On the local and superlinear convergence of Quasi-Newton methods . J. Inst. Maths. Applics. , 12 : 223 – 245 .
   Google Scholar
• Dennis , J. E. Jr . 1971 . On the convergence of Broyden's method for nonlinear systems of equations . Math. Comput. , 25 : 559 – 567 .
   Web of Science ®Google Scholar
• Dennis , J. E. Jr. and Moré Jorge , J. 1977 . Quasi-Newton methods, motivation and theory . SIAM Review , 19 ( 1 ) : 46 – 89 .
   Web of Science ®Google Scholar
• Häuβler , W. M. 1986 . A Kantorovich-type convergence analysis for the Gauss-Newton method . Numer. Math. , 48 : 119 – 125 .
   Google Scholar
• Ichim , I. 1982 . Sur une probleme de minimum . Rev. Roum. Math. Pures et. Appl. , 27 ( 9 ) : 969 – 979 .
   Google Scholar
• Kim , S. and Tewarson , R. P. 1992 . A Quasi-Newton method for solving non-linear algebraic equations . Computers Math. Applic. , 24 ( 4 ) : 93 – 97 .
   Web of Science ®Google Scholar
• Kim , S. and Tewarson , R. P. 1995 . The convergence of Quasi-Gauss-Newton Methods for Nonlinear Problems . Computers Math. Applic. , 29 ( 8 ) : 27 – 38 .
   Web of Science ®Google Scholar
• Moore , E. H. 1919/20 . On the reciprocal of the general algebraic matrix . Bull. Am. Math. Soc. , 26 : 394 – 395 .
   Google Scholar
• Lawson , C. L. and Hanson , R. J. 1974 . Solving least squares problems , Englewood Cliffs, NJ : Prentice Hall .
   Google Scholar
• Ortega , J. M. and Rheinboldt , W. C. 1970 . Iterative solution of nonlinear equations in several variables , London, NY : Academic Press .
   Google Scholar
• Penrose , R. 1955 . A generalized inverse for matrices . Proc. Camb. Phil. Soc. , 51 : 406 – 413 .
   Google Scholar