Vandermonde Matrices on the Circle: Spectral Properties and Conditioning.
W. Gautschi, A. Córdova, ... (1990)
Numerische Mathematik
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Displaying similar documents to “Spectral Methods with Sparse Matrices.”
Vandermonde Matrices on the Circle: Spectral Properties and Conditioning.
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In this paper we show new formulas for the spectral radius and the spectral subradius of a set of matrices. The advantage of our results is that we express the spectral radius of any set of matrices by the spectral radius of a set of symmetric positive definite matrices. In particular, in one of our formulas the spectral radius is expressed by singular eigenvalues of matrices, whereas in the existing results it is expressed by eigenvalues.
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The joint spectral radius of a finite set of real matrices is defined to be the maximum possible exponential rate of growth of products of matrices drawn from that set. In previous work with K. G. Hare and J. Theys we showed that for a certain one-parameter family of pairs of matrices, this maximum possible rate of growth is attained along Sturmian sequences with a certain characteristic ratio which depends continuously upon the parameter. In this note we answer some open questions...
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