### Can Any Stationary Iteration Using Linear Information Be Globally Convergent?Can Any Stationary Iteration Using Linear Information Be Globally Convergent?

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 Author Wasilkowski, G. W. Source ACM Digital Library Content type Text Publisher Association for Computing Machinery (ACM) File Format PDF Copyright Year ©1980 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science Abstract All known globally convergent iterations for the solution of a nonlinear operator equation $ƒ(\textit{x})$ = 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 $\textit{no}$ 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. ISSN 00045411 Age Range 18 to 22 years ♦ above 22 year Educational Use Research Education Level UG and PG Learning Resource Type Article Publisher Date 1980-04-01 Publisher Place New York e-ISSN 1557735X Journal Journal of the ACM (JACM) Volume Number 27 Issue Number 2 Page Count 7 Starting Page 263 Ending Page 269

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Source: ACM Digital Library