The Convergence of Multipoint Iterations to Multiple Zeros,
Abstract
The paper fills a gap in the theory of multipoint iteration function exemplified by the question: how does the secant method converge to a multiple zero. A general theory of the linear convergence of multipoint iterations is developed, and it is shown that two broad classes of iterative methods fit this theory. The results of numerical investigations based on the theory suggest that Muller's method applied to a multiple zero will inevitably produce complex iterates. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1973
- Accession Number
- AD0755229
Entities
People
- G. W. Stewart
Organizations
- Carnegie Mellon University