home *** CD-ROM | disk | FTP | other *** search
/ NetNews Usenet Archive 1992 #27 / NN_1992_27.iso / spool / sci / math / numanal / 3342 < prev    next >
Encoding:
Text File  |  1992-11-18  |  1.1 KB  |  32 lines
  1. Newsgroups: sci.math.num-analysis
  2. Path: sparky!uunet!caen!takriti
  3. From: takriti@engin.umich.edu (samer Takriti)
  4. Subject: Re: Help required to solve a system of non-linear Eq.,s
  5. Message-ID: <k5F=yL=@engin.umich.edu>
  6. Date: Wed, 18 Nov 92 12:48:52 EST
  7. Organization: University of Michigan Engineering, Ann Arbor
  8. References: <1992Nov18.024417.19684@oucsace.cs.ohiou.edu>
  9. Keywords: Newton - Raphson method(currently used)
  10. Nntp-Posting-Host: ephedra.engin.umich.edu
  11. Lines: 19
  12.  
  13. In article <1992Nov18.024417.19684@oucsace.cs.ohiou.edu> ravi@bobcat.ent.ohiou.edu (Pattalachinti) writes:
  14. >Are there any thumb-rules for the successful execution of
  15. >Newton-Raphson method to work successfully on a non-linear
  16. >system of equations.
  17. >
  18. >Any suggestion is welcome,
  19. >
  20. >Thanking in advance,
  21. >
  22. >Ravi 
  23.  
  24. I think that what you are looking for is "Kantarovitch theorem". It states
  25. that if the function is continuously differentiable, the norm of the e
  26. inverse of the Jacobian is less than beta, and the norm of the (J^{-1}F(x))
  27. is less than eta (J is the jacobian) then
  28. if alpha * beta * eta <= .5 then the sequence converges.
  29. F is lipschitz continuous with constant alpha.
  30. -Samer
  31.  
  32.