Computation of the eigenvalues of convexity preserving matrices (Q1021865)
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scientific article; zbMATH DE number 5563148
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Computation of the eigenvalues of convexity preserving matrices |
scientific article; zbMATH DE number 5563148 |
Statements
Computation of the eigenvalues of convexity preserving matrices (English)
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9 June 2009
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Matrices which are \(r\)-convexity preserving for \(r=0,1,\dots,k\) arise in many practical and theoretical problems. A source of many examples is provided by the collocation matrices of \(r\)-convexity preserving systems of functions. Based on results of \textit{J. M. Carnicer}, \textit{M. García-Esnaola} and \textit{J. M. Penã} [Comput. Aided Geom. Des. 13, No. 2, 179--197 (1996; Zbl 0900.68404)], in this paper, a direct method for computing the \(k\) largest eigenvalues of the \(r\)-convexity matrices is proposed. For an \(n\times n\) matrix, the computational cost is \(O(kn^2)\).
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\(r\)-convexity preserving matrix
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eigenvalues
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explicit formula
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directed method
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convexity
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