Result: Bounding Perturbations in Zeros of Nonlinear Systems: Bounding perturbations in zeros of nonlinear systems

Title:
Bounding Perturbations in Zeros of Nonlinear Systems: Bounding perturbations in zeros of nonlinear systems
Authors:
Michael A. Wolfe
Source:
Reliable Computing. 8:177-188
Publisher Information:
Springer Science and Business Media LLC, 2002.
Publication Year:
2002
Subject Terms:
zeros of nonlinear systems, numerical examples, Numerical computation of solutions to systems of equations, nonlinear equations, interval arithmetic, 0101 mathematics, 01 natural sciences
Document Type:
Academic journal Article
File Description:
application/xml
Language:
English
ISSN:
1573-1340
1385-3139
DOI:
10.1023/a:1015559628657
Access URL:
https://link.springer.com/article/10.1023%2FA%3A1015559628657
https://dblp.uni-trier.de/db/journals/rc/rc8.html#Wolfe02
Rights:
Springer Nature TDM
Accession Number:
edsair.doi.dedup.....dff1b953734d0b946e8c0aec7d283f9d
Database:
OpenAIRE

Further Information

The work is devoted to determines computationally rigorous bounds on solutions \(x\in \mathbb{R}^n\) of nonlinear equations \(F(x,t) =0\in \mathbb{R}^m\), \(m\leq n\), due to small perturbations in the parameter \(t\in \mathbb{R}^l\). Conditions for existence and uniqueness of solutions are given. The obtained algorithms are illustrated by several numerical examples.