Can Any Stationary Iteration Using Linear Information Be Globally Convergent?
 Title:
 Can Any Stationary Iteration Using Linear Information Be Globally Convergent?
 Author(s):
 Wasilkowski, Grzegorz W.
 Date:
 1980
 Type:
 Technical reports
 Department(s):
 Computer Science
 Persistent URL:
 http://hdl.handle.net/10022/AC:P:11495
 Series:
 Columbia University Computer Science Technical Reports
 Part Number:
 CUCS14380
 Publisher:
 Department of Computer Science, Columbia University
 Publisher Location:
 New York
 Abstract:
 All known globally convergent iterations for the solution of a nonlinear operator equation f(x) = 0 are either nonstationary or use nonlinear information. It is asked whether there exists a globally convergent stationary iteration which uses linear information. It is proved that even if global convergence is defined in a weak sense, there exists no such iteration for as simple a class of problems as the set of all analytic complex functions having only simple zeros. It is conjectured that even for the class of all real polynomials which have real simple zeros there does not exist a globally convergent stationary iteration using linear information.
 Subject(s):
 Computer science
 Item views
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 Suggested Citation:
 Grzegorz W. Wasilkowski, 1980, Can Any Stationary Iteration Using Linear Information Be Globally Convergent?, Columbia University Academic Commons, http://hdl.handle.net/10022/AC:P:11495.