Minimal Perturbations to Roots of Parameterized Equations
Joseph F. Grcar
TL;DR
This paper demonstrates that minimal perturbations to roots of parameterized equations can be effectively estimated using linear approximations, simplifying the analysis of stability and sensitivity.
Contribution
It introduces a method to estimate minimal perturbations from linearizations, providing a practical approach to analyze root stability.
Findings
Linearizations reliably estimate minimal perturbations.
The approach simplifies stability analysis of parameterized equations.
Potential applications in numerical analysis and control systems.
Abstract
The size of minimal perturbations to roots of parameterized equations can be estimated reliably from linearizations of the equations.
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Taxonomy
TopicsNumerical methods for differential equations · Stability and Controllability of Differential Equations