Accession Number:

ADA064295

Title:

Can Any Stationary Iteration Using Linear Information be Globally Convergent.

Descriptive Note:

Interim rept.,

Corporate Author:

CARNEGIE-MELLON UNIV PITTSBURGH PA DEPT OF COMPUTER SCIENCE

Personal Author(s):

• Wasilkowski,G. W.

Report Date:

1978-12-01

Pagination or Media Count:

22.0

Abstract:

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

Descriptors:

• *OPERATORS(MATHEMATICS)
• *ITERATIONS
• GLOBAL
• NONLINEAR DIFFERENTIAL EQUATIONS
• POLYNOMIALS
• CONVERGENCE

Subject Categories:

• Numerical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE