Comparative results on eigenvalues,pseudospectra and conditionspectra

Abstract

Conditionspectrum measures the computational stability of solving a linear system. In this paper, ten theorems involving ε-conditionspectrum are presented. All these theorems generalize a well known eigenvalue theorem and simultaneously compare with an appropriate pseudospectra theorem. Our organizing principle is that each conditionspectrum result precisely reduces to the corresponding eigenvalue theorem when ε = 0. The format of each conditionspectrum result is similar to the pseudospectrum result for easy comparison. Each condition spectrum is formatted similar to pseudospectrum result for the easy comparison.