Matrix norms and their sensitivity to noise a computational study

Authors:
M. O. Abdalla
Affiliations:
Department of Mechanical Engineering, University of Jordan, Amman, Jordan
Venue:
ISTASC'05 Proceedings of the 5th WSEAS/IASME International Conference on Systems Theory and Scientific Computation
Year:
2005

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Abstract

Most of the objective (cost) functions in optimization techniques utilize norms especially when dealing with signals, vectors, or matrices. In this work, three norms were studied, namely matrix One norm, Infinity norm, and Frobenius (Euclidean or Two) norm. The effect of noise on these matrix norms was studied with the aid of a generalized eigen equation. Basic analysis of the effect of noise on matrix norms is provided, which is also complimented with a computer simulated results. It turns out that the Frobenius norm is the least sensitive norm to noise.