Can Any Stationary Iteration Using Linear Information be Globally Convergent.
CARNEGIE-MELLON UNIV PITTSBURGH PA DEPT OF COMPUTER SCIENCE
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All known globally convergent interations for the solution of a nonlinear operator equation fx 0 are either non-stationary or use nonlinear information. We ask whether there exists a globally convergent stationary iteration which uses linear information. We prove 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. We conjecture 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. Author
- Numerical Mathematics