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Distance bounds for prescribed multiple eigenvalues of matrix polynomials

โœ Scribed by Panayiotis J. Psarrakos


Book ID
113772237
Publisher
Elsevier Science
Year
2012
Tongue
English
Weight
548 KB
Volume
436
Category
Article
ISSN
0024-3795

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๐Ÿ“œ SIMILAR VOLUMES


The distance from a matrix polynomial to
โœ Nikolaos Papathanasiou; Panayiotis Psarrakos ๐Ÿ“‚ Article ๐Ÿ“… 2008 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 803 KB

For a matrix polynomial P (ฮป) and a given complex number ฮผ, we introduce a (spectral norm) distance from P (ฮป) to the matrix polynomials that have ฮผ as an eigenvalue of geometric multiplicity at least ฮบ, and a distance from P (ฮป) to the matrix polynomials that have ฮผ as a multiple eigenvalue. Then w

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An error bound for approximate eigenvalues of a complex n-dimensional pencil (A, B) is given. From our theorem several well-known bounds follow as corollaries. Our result takes into account the general residual AX -BXW, where X ~ C n x m and W ~ C mxm with m ~< n.

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Bounds are derived for the real eigenvalues of a special matrix. Matrices of this form arise in the design of two-up one-down cascades for isotope separation.