Average-Case Perturbations and Smooth Condition Numbers
arXiv:0812.2260h-index: 9
Originality Synthesis-oriented
AI Analysis
Provides a new theoretical tool for analyzing stability in numerical problems, but the contribution is primarily theoretical and incremental.
The paper introduces a condition number for directionally uniform perturbations, establishes its relationship with the classical condition number, and demonstrates its applicability across a broad class of problems.
We define a new condition number adapted to directionally uniform perturbations. The definitions and theorems can be applied to a large class of problems. We show the relation with the classical condition number, and study some interesting examples.