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A bound for the condition of a hyperbolic eigenvector matrix

✍ Scribed by Ivan Slapničar; Krešimir Veselić

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
317 KB
Volume
290
Category
Article
ISSN
0024-3795

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✦ Synopsis

The hyperbolic eigenvector matrix is a matrix X which simultaneously diagonalizes the pair (H,J), where H is Hermitian positive definite and J = diag(:E1) such that X*HX = A and X*JX = J. We prove that the spectral condition of X, r(X), is bounded by K(X) ~< ~/min x(D*HD), where the minimum is taken over all non-singular matrices D which commute with J. This bound is attainable and it can be simply computed. Similar results hold for other signature matrices J, like in the discretized Klein-Gordon equation.

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