Numerical Stability for Solving Nonlinear Equations,
Abstract
The concepts of the condition number, numerical stability and well-behavior for solving systems of nonlinear equations F(x) = 0 are introduced. Necessary and sufficient conditions for numerical stability and well-behavior of a stationary iteration are given. The author proves numerical stability and well-behavior of the Newton iteration for solving systems of equations and of some variants of secant iteration for solving a single equation under a natural assumption on the computed evaluation of F. Furthermore it is shown that the Steffensen iteration is unstable and it is shown how to modify it to have well-behavior and hence stability.
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 01, 1975
- Accession Number
- ADA006862
Entities
People
- H. Wozniakowski
Organizations
- Carnegie Mellon University