Abstract
In this paper we consider the eigen pair set
where [A] is a given real n x n interval matrix (cf. Alefeld and Herzberger (1983), e.g., for interval analysis) and \(\mathcal{P}\) is some fixed property such as symmetry, Toeplitz form, etc.. Before we study this set in greater detail we mention other ones which are related to it: When dealing with systems of linear equations
(ℝn x n set of real n x n matrices, ℝn set of real vectors with n components) there sometimes occurs the problem of varying the input data \(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{A} ,\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{b} \) within certain tolerances and looking for the set S of the resulting solutions x*.
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Alefeld, G., Kreinovich, V., Mayer, G. (2001). Modifications of the Oettli-Prager Theorem with Application to the Eigenvalue Problem. In: Alefeld, G., Rohn, J., Rump, S., Yamamoto, T. (eds) Symbolic Algebraic Methods and Verification Methods. Springer, Vienna. https://doi.org/10.1007/978-3-7091-6280-4_3
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DOI: https://doi.org/10.1007/978-3-7091-6280-4_3
Publisher Name: Springer, Vienna
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