Properties of a matrix with a very ill-conditioned eigenproblem
- Dr. Axel Ruhe
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It is proved that a matrix that has a very ill-conditioned eigenvector matrix is close to one that has multiple eigenvalues, and an estimate of this distance is given, measured in the Euclidean matrix norm.
Supplementary Material (0)
- Henrici, P.: Bounds for iterates, inverses, spectral variation and fields of values of non-normal matrices. Num. Math.4, 24–40 (1962).
- Householder, A. S.: The theory of matrices in numerical analysis. New York:Blaisdell, 1st Ed., 1964.
- Varah, J. M.: Computing invariant subspaces of a general matrix when the eigen-system is poorly conditioned, to appear.
- Wilkinson, J. H.: The algebraic eigenvalue problem. Oxford: Clarendon Press, 1st Ed., 1965.
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- Properties of a matrix with a very ill-conditioned eigenproblem
Volume 15, Issue 1 , pp 57-60
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- Dr. Axel Ruhe (1)
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- 1. Lunds Universitet, Institutionen för Informationsbehandling, Sölvegatan 14A, 22362, Lund, Sweden