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:

Computer Science

Permanent 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
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