Comparative results on eigenvalues,pseudospectra and conditionspectra

Details Comparative results on eigenvalues,pseudospectra and conditionspectra Comparative results on eigenvalues,pseudospectra and conditionspectra

2011-09-13

arxiv.org/abs/1109.2731v1

Mathematics

Spectral Theory

9 Pages

Scientific paper

Conditionspectrum measures the computational stability of solving a linear system. In this paper, ten theorems involving {\epsilon}-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 {\epsilon} = 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.

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